Finite Group Databasebeta

← #13140248

Subgroups — #13140248

Order 1728.

909 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6198C211yesmaximal, characteristic
2C2×#3752⋊C3C211yesmaximal, characteristic, complemented
3C2×#3752⋊C3C211yesmaximal, characteristic, complemented
4C2×#88450C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6C2×#88448C211yesmaximal, characteristic, complemented
7#11720574C211yesmaximal, characteristic, complemented
8#10591312—31nomaximal
9#10591292—31nomaximal
10C23×(C3⋊D3)⋊C3C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C22×#1084C2211yescharacteristic
15C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
16C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
17C2×#6198—22no—
18C2×#6198—22no—
19C2×#6198—22no—
20#3752⋊C3—22no—
21#3752⋊C3—22no—
22#88450—22no—
23#88450—22no—
24#88448—22no—
25C22×#626—31no—
26C22×#626—31no—
27C2×#3752D311yescharacteristic, complemented
28C2×#3752D311yescharacteristic, complemented
29C2×C3×(C2×D3)⋊C4—31no—
30C2×C3×(C2×D3)⋊C4—31no—
31C2×#3724—31no—
32C2×Dic3⋊Dic3—31no—
33C2×#3722—31no—
34C2×#3722—31no—
35C2×(C2×D3)⋊Dic3—31no—
36C2×(C2×D3)⋊Dic3—31no—
37C3×C3⋊#95—31no—
38C3×C3⋊#95—31no—
39C3×C3⋊#95—61no—
40C23×H(3,𝔽3)C2311yescharacteristic
41C22×(C3⋊D3)⋊C3—21no—
42C22×(C3⋊D3)⋊C3—21no—
43C22×(C3⋊D3)⋊C3—21no—
44C22×(C3⋊D3)⋊C3—21no—
45C22×(C3⋊D3)⋊C3—21no—
46C22×(C3⋊D3)⋊C3—21no—
47C22×(C3⋊D3)⋊C3—21no—
48C22×(C3⋊D3)⋊C3—21no—
49C22×(C3⋊D3)⋊C3—21no—
50C22×(C3⋊D3)⋊C3—21no—
51C22×(C3⋊D3)⋊C3—21no—
52C22×(C3⋊D3)⋊C3—21no—
53C22×(C3⋊D3)⋊C3D412yes—
54C22×(C3⋊D3)⋊C3D412yes—
55C2×C4×H(3,𝔽3)—21no—
56C2×C4×H(3,𝔽3)—21no—
57C2×C4×H(3,𝔽3)—21no—
58C2×#1084—21no—
59C2×#1084—21no—
60C2×#1084—21no—
61C2×#1084—21no—
62C2×#1084—21no—
63C2×#1084D412yes—
64C2×(C3⋊Dic3)⋊C3—21no—
65C2×(C3⋊Dic3)⋊C3—21no—
66C2×(C3⋊Dic3)⋊C3—21no—
67C2×(C3⋊Dic3)⋊C3—21no—
68C2×(C3⋊Dic3)⋊C3—21no—
69C2×(C3⋊Dic3)⋊C3D412yescomplemented
70#6198—28no—
71#4961—91no—
72#4959—91no—
73#4672—91no—
74C23×C3⋊D3C2×D311yescharacteristic
75C23×C3⋊D3C2×D311yescharacteristic
76C23×C3×D3—31no—
77C23×C3×D3—31no—
78C22×C32×C4—21no—
79C22×C32×C4C2×D311yescharacteristic
80C22×C32×C4C2×D311yescharacteristic
81C22×C3⋊Dic3C2×D311yescharacteristic
82C22×C3⋊Dic3C2×D311yescharacteristic
83C22×C3×Dic3—31no—
84C22×C3×Dic3—31no—
85C22×C3×Dic3—31no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—61no—
90C22×C3×Dic3—61no—
91C2×#626—62no—
92C2×#626—62no—
93C2×#626—62no—
94C2×#626—62no—
95C2×#626—62no—
96C2×#626—62no—
97#3752—22no—
98#3752—22no—
99C3×(C2×D3)⋊C4—62no—
100C3×(C2×D3)⋊C4—62no—
101#3724—62no—
102Dic3⋊Dic3—62no—
103#3722—62no—
104#3722—62no—
105(C2×D3)⋊Dic3—62no—
106(C2×D3)⋊Dic3—62no—
107C22×H(3,𝔽3)C2×D411yescharacteristic
108C22×H(3,𝔽3)C2×D411yescharacteristic
109C22×H(3,𝔽3)C2×D411yescharacteristic
110C22×H(3,𝔽3)C2×D411yescharacteristic
111C22×H(3,𝔽3)#4111yescharacteristic
112C22×H(3,𝔽3)#4111yescharacteristic
113C22×H(3,𝔽3)#4111yescharacteristic
114C2×(C3⋊D3)⋊C3—22no—
115C2×(C3⋊D3)⋊C3—22no—
116C2×(C3⋊D3)⋊C3—22no—
117C2×(C3⋊D3)⋊C3—22no—
118C2×(C3⋊D3)⋊C3—22no—
119C2×(C3⋊D3)⋊C3—22no—
120C2×(C3⋊D3)⋊C3—41no—
121C2×(C3⋊D3)⋊C3—41no—
122C2×(C3⋊D3)⋊C3—41no—
123C2×(C3⋊D3)⋊C3—41no—
124C2×(C3⋊D3)⋊C3—41no—
125C2×(C3⋊D3)⋊C3—41no—
126C2×(C3⋊D3)⋊C3—41no—
127C2×(C3⋊D3)⋊C3—41no—
128C4×H(3,𝔽3)—41no—
129#1084—22no—
130#1084—41no—
131(C3⋊Dic3)⋊C3—22no—
132(C3⋊Dic3)⋊C3—41no—
133C22×#67—91no—
134C22×#67—91no—
135C22×D12—91no—
136C2×C3×C22⋊C4—91no—
137C2×C3×C22⋊C4—91no—
138C2×#217—91no—
139C2×#217—91no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—91no—
143C2×(C2×D3)⋊C4—91no—
144C2×(C2×D3)⋊C4—91no—
145C2×(C2×D3)⋊C4—91no—
146C2×(C2×D3)⋊C4—91no—
147C2×(C2×D3)⋊C4—91no—
148C2×C4⋊Dic3—91no—
149C2×Dic3⋊C4—91no—
150C2×Dic3⋊C4—91no—
151C3×#95—91no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—61no—
155C23×C32—21no—
156C23×C32C22×D311yescharacteristic
157C23×C32C22×D311yescharacteristic
158C22×C3⋊D3—21no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3D1212yes—
171C22×C3⋊D3#6712yes—
172C22×C3×D3—32no—
173C22×C3×D3—32no—
174C22×C3×D3—61no—
175C22×C3×D3—61no—
176C22×C3×D3—61no—
177C22×C3×D3—61no—
178C22×C3×D3—61no—
179C22×C3×D3—61no—
180C22×C3×D3—61no—
181C22×C3×D3—61no—
182C22×C3×D3—61no—
183C22×C3×D3—61no—
184C22×C3×D3—61no—
185C22×C3×D3—61no—
186C2×C32×C4—22no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—41no—
194C2×C32×C4—41no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3#6712yescomplemented
201C2×C3×Dic3—32no—
202C2×C3×Dic3—32no—
203C2×C3×Dic3—32no—
204C2×C3×Dic3—62no—
205C2×C3×Dic3—61no—
206C2×C3×Dic3—61no—
207C2×C3×Dic3—61no—
208C2×C3×Dic3—61no—
209C2×C3×Dic3—61no—
210C2×C3×Dic3—61no—
211C2×C3×Dic3—62no—
212C2×C3×Dic3—61no—
213C2×C3×Dic3—61no—
214C2×C3×Dic3—61no—
215C2×C3×Dic3—61no—
216C2×C3×Dic3—61no—
217C2×C3×Dic3—61no—
218C2×C3×Dic3—61no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—121no—
222C2×C3×Dic3—121no—
223C2×C3×Dic3—121no—
224C2×C3×Dic3—121no—
225#626—68no—
226#626—68no—
227#394—271noSylow
228C2×H(3,𝔽3)#12011yescharacteristic
229C2×H(3,𝔽3)#12111yescharacteristic
230C2×H(3,𝔽3)#12111yescharacteristic
231C2×H(3,𝔽3)#12111yescharacteristic
232C2×H(3,𝔽3)#12311yescharacteristic
233C2×H(3,𝔽3)#12311yescharacteristic
234C2×H(3,𝔽3)#12411yescharacteristic
235(C3⋊D3)⋊C3—42no—
236(C3⋊D3)⋊C3—42no—
237C24×C3—91no—
238C24×C3—91no—
239C23×D3—31no—
240C23×D3—31no—
241C23×D3—91no—
242C23×D3—91no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—61no—
246C22×C3×C4—91no—
247C22×C3×C4—91no—
248C22×C3×C4—91no—
249C22×C3×C4—91no—
250C22×C3×C4D3211yescharacteristic
251C2×#67—182no—
252C2×#67—182no—
253C2×#67—182no—
254C2×#67—182no—
255C2×#67—182no—
256C2×#67—182no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—61no—
264C22×Dic3—61no—
265C22×Dic3—91no—
266C22×Dic3—91no—
267C2×D12—182no—
268C2×D12—182no—
269C2×D12—182no—
270C3×C22⋊C4—182no—
271C3×C22⋊C4—182no—
272#217—182no—
273#217—182no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—182no—
277(C2×D3)⋊C4—182no—
278(C2×D3)⋊C4—182no—
279(C2×D3)⋊C4—182no—
280(C2×D3)⋊C4—182no—
281(C2×D3)⋊C4—182no—
282C4⋊Dic3—182no—
283Dic3⋊C4—182no—
284Dic3⋊C4—182no—
285C22×C32—21no—
286C22×C32—21no—
287C22×C32—21no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32C2×D1211yescharacteristic
293C22×C32#23511yescharacteristic
294C22×C32#23511yescharacteristic
295C22×C32#23511yescharacteristic
296C22×C32D3×D411yescharacteristic
297C22×C32D3×D411yescharacteristic
298C22×C32D3×D411yescharacteristic
299C22×C32D3×D411yescharacteristic
300C22×C32D3×D411yescharacteristic
301C22×C32#23711yescharacteristic
302C22×C32#23711yescharacteristic
303C22×C32#23711yescharacteristic
304C22×C32C2×#6711yescharacteristic
305C22×C32C2×#6711yescharacteristic
306C2×C3⋊D3—22no—
307C2×C3⋊D3—22no—
308C2×C3⋊D3—22no—
309C2×C3⋊D3—22no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C2×C3⋊D3—41no—
320C2×C3×D3—62no—
321C2×C3×D3—62no—
322C2×C3×D3—62no—
323C2×C3×D3—62no—
324C2×C3×D3—62no—
325C2×C3×D3—62no—
326C2×C3×D3—121no—
327C2×C3×D3—121no—
328C2×C3×D3—121no—
329C2×C3×D3—121no—
330C2×C3×D3—121no—
331C2×C3×D3—121no—
332C2×C3×D3—121no—
333C2×C3×D3—121no—
334C32×C4—42no—
335C32×C4—41no—
336C32×C4—41no—
337C3⋊Dic3—22no—
338C3⋊Dic3—41no—
339C3×Dic3—62no—
340C3×Dic3—62no—
341C3×Dic3—62no—
342C3×Dic3—122no—
343C3×Dic3—122no—
344C3×Dic3—121no—
345C3×Dic3—121no—
346C3×Dic3—121no—
347C22×D4—271no—
348C2×C4⋊C4—271no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—91no—
351C2×C22⋊C4—271no—
352C2×C22⋊C4—271no—
353#95—91no—
354H(3,𝔽3)#39411yescharacteristic, complemented, Sylow
355C23×C3—31no—
356C23×C3—31no—
357C23×C3—61no—
358C23×C3—92no—
359C23×C3—92no—
360C23×C3—181no—
361C23×C3—181no—
362C23×C3—181no—
363C23×C3—181no—
364C23×C3—181no—
365C23×C3—181no—
366C23×C3—181no—
367C23×C3—181no—
368C23×C3—181no—
369C23×C3—181no—
370C23×C3—181no—
371C23×C3—181no—
372C23×C3C2×D3211yescharacteristic
373C22×D3—32no—
374C22×D3—32no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—61no—
387C22×D3—92no—
388C22×D3—92no—
389C22×D3—181no—
390C22×D3—181no—
391C22×D3—181no—
392C22×D3—181no—
393C22×D3—181no—
394C22×D3—181no—
395C22×D3—181no—
396C22×D3—181no—
397C22×D3—181no—
398C22×D3—181no—
399C22×D3—181no—
400C22×D3—181no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—62no—
411C2×C3×C4—92no—
412C2×C3×C4—92no—
413C2×C3×C4—121no—
414C2×C3×C4—121no—
415C2×C3×C4—181no—
416C2×C3×C4—181no—
417C2×C3×C4—181no—
418C2×C3×C4—181no—
419C2×C3×C4—181no—
420C2×C3×C4—181no—
421C2×C3×C4—181no—
422C2×C3×C4—181no—
423C2×C3×C4—181no—
424C2×C3×C4—181no—
425#67—188no—
426#67—188no—
427C2×Dic3—32no—
428C2×Dic3—32no—
429C2×Dic3—32no—
430C2×Dic3—62no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—62no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—92no—
448C2×Dic3—121no—
449C2×Dic3—121no—
450C2×Dic3—121no—
451C2×Dic3—121no—
452C2×Dic3—181no—
453C2×Dic3—181no—
454C2×Dic3—181no—
455C2×Dic3—181no—
456C2×Dic3—181no—
457D12—188no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32#88211yescharacteristic
466C2×C32#88311yescharacteristic
467C2×C32#88311yescharacteristic
468C2×C32#88411yescharacteristic
469C2×C32#88411yescharacteristic
470C2×C32#88511yescharacteristic
471C2×C32#88511yescharacteristic
472C2×C32#88611yescharacteristic
473C2×C32#92911yescharacteristic
474C2×C32#93011yescharacteristic
475C2×C32#93711yescharacteristic
476C2×C32#93811yescharacteristic
477C2×C32#93911yescharacteristic
478C2×C32#93911yescharacteristic
479C3⋊D3—42no—
480C3⋊D3—42no—
481C3×D3—122no—
482C3×D3—122no—
483C24—91no—
484C24—91no—
485C2×D4—542no—
486C2×D4—542no—
487C2×D4—542no—
488C22×C4—91no—
489C22×C4—91no—
490C22×C4—91no—
491C22×C4—91no—
492C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
493C4⋊C4—542no—
494C22⋊C4—182no—
495C22⋊C4—182no—
496C22⋊C4—542no—
497C22⋊C4—542no—
498C22×C3—31no—
499C22×C3—31no—
500C22×C3—31no—
501C22×C3—31no—
502C22×C3—31no—
503C22×C3—31no—
504C22×C3—31no—
505C22×C3—31no—
506C22×C3—31no—
507C22×C3—31no—
508C22×C3—31no—
509C22×C3—31no—
510C22×C3—31no—
511C22×C3—31no—
512C22×C3—61no—
513C22×C3—61no—
514C22×C3—61no—
515C22×C3—61no—
516C22×C3—61no—
517C22×C3—61no—
518C22×C3—61no—
519C22×C3—182no—
520C22×C3—182no—
521C22×C3—182no—
522C22×C3—182no—
523C22×C3—182no—
524C22×C3—182no—
525C22×C3—361no—
526C22×C3—361no—
527C22×C3—361no—
528C22×C3—361no—
529C22×C3—361no—
530C22×C3—361no—
531C22×C3—361no—
532C22×C3—361no—
533C22×C3#379511yescharacteristic
534C22×C3#379811yescharacteristic
535C22×C3D3×D1211yescharacteristic
536C22×C3#380211yescharacteristic
537C22×C3#380511yescharacteristic
538C22×C3D3×#6711yescharacteristic
539C22×C3D3×#6711yescharacteristic
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
549C2×D3—121no—
550C2×D3—121no—
551C2×D3—121no—
552C2×D3—121no—
553C2×D3—121no—
554C2×D3—182no—
555C2×D3—182no—
556C2×D3—182no—
557C2×D3—182no—
558C2×D3—182no—
559C2×D3—182no—
560C2×D3—361no—
561C2×D3—361no—
562C2×D3—361no—
563C2×D3—361no—
564C2×D3—361no—
565C2×D3—361no—
566C2×D3—361no—
567C2×D3—361no—
568C3×C4—41no—
569C3×C4—121no—
570C3×C4—121no—
571C3×C4—122no—
572C3×C4—182no—
573C3×C4—182no—
574C3×C4—361no—
575C3×C4—361no—
576Dic3—62no—
577Dic3—62no—
578Dic3—62no—
579Dic3—122no—
580Dic3—121no—
581Dic3—121no—
582Dic3—122no—
583Dic3—121no—
584Dic3—182no—
585Dic3—361no—
586C32—21no—
587C32#495911yescharacteristic, complemented
588C32#496111yescharacteristic, complemented
589C23—92no—
590C23—92no—
591C23—181no—
592C23—181no—
593C23—181no—
594C23—181no—
595C23—181no—
596C23—181no—
597C23—181no—
598C23—181no—
599C23—181no—
600C23—181no—
601C23—181no—
602C23—181no—
603C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
604D4—548no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—92no—
609C2×C4—92no—
610C2×C4—181no—
611C2×C4—181no—
612C2×C4—181no—
613C2×C4—181no—
614C2×C4—181no—
615C2×C4—181no—
616C2×C4—181no—
617C2×C4—181no—
618C2×C4—181no—
619C2×C4—181no—
620C2×C3—31no—
621C2×C3—31no—
622C2×C3—31no—
623C2×C3—31no—
624C2×C3—31no—
625C2×C3—31no—
626C2×C3—31no—
627C2×C3—31no—
628C2×C3—31no—
629C2×C3—31no—
630C2×C3—31no—
631C2×C3—31no—
632C2×C3—31no—
633C2×C3—31no—
634C2×C3—61no—
635C2×C3—61no—
636C2×C3—61no—
637C2×C3—61no—
638C2×C3—61no—
639C2×C3—61no—
640C2×C3—61no—
641C2×C3—362no—
642C2×C3—362no—
643C2×C3#6388511yescharacteristic
644C2×C3#6389111yescharacteristic
645C2×C3#6390511yescharacteristic
646C2×C3#6390611yescharacteristic
647C2×C3#6391511yescharacteristic
648C2×C3#6392211yescharacteristic
649C2×C3#6397011yescharacteristic
650D3—122no—
651D3—122no—
652D3—362no—
653D3—362no—
654C22—182no—
655C22—182no—
656C22—182no—
657C22—182no—
658C22—182no—
659C22—182no—
660C22—361no—
661C22—361no—
662C22—361no—
663C22—361no—
664C22—361no—
665C22—361no—
666C22—361no—
667C22—361no—
668C22#8864811yescharacteristic
669C22#8865011yescharacteristic
670C22#8865411yescharacteristic
671C22#8865511yescharacteristic
672C22#8867211yescharacteristic
673C22#8867611yescharacteristic
674C22#8867611yescharacteristic
675C4—41no—
676C4—182no—
677C4—182no—
678C4—361no—
679C4—361no—
680C3—31no—
681C3—31no—
682C3—61no—
683C3#1059139011yescharacteristic
684C2—362no—
685C2—362no—
686C2#1172112611yescharacteristic
687C2#1172113111yescharacteristic
688C2#1172113911yescharacteristic
689C2#1172114011yescharacteristic
690C2#1172114511yescharacteristic
691C2#1172116211yescharacteristic
692C2#1172131311yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC23×H(3,𝔽3)C23
Frattini, socleC23×C3C2×D32
FittingC22×C4×H(3,𝔽3)C22
prime radicalC22×#6198C2
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#394
LCSG ▷ C23×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#3752⋊C3C2semidirect
3. C2×#3752⋊C3C2semidirect
4. C2×#88450C2semidirect
5. C2×#88450C2semidirect
6. C2×#88448C2semidirect
7. #11720574C2semidirect
27. C2×#3752D3semidirect
28. C2×#3752D3semidirect
69. C2×(C3⋊Dic3)⋊C3D4semidirect
200. C2×C3⋊Dic3#67semidirect
354. H(3,𝔽3)#394semidirect
587. C32#4959semidirect
588. C32#4961semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#61982
C2×#3752⋊C32
C2×#884502
C2×#884482
#117205742
#105913123
#105912923