Subgroups — #30839279

Order 17152.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22571536	C₂	1	2	yes	maximal, complemented
2	#22570788	C₂	1	1	yes	maximal, characteristic, complemented
3	#22569184	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559738	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559733	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559694	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559689	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559626	C₂	1	2	yes	maximal, complemented
9	#22559619	C₂	1	2	yes	maximal, complemented
10	#22558902	C₂	1	2	yes	maximal, complemented
11	C₂×#334×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863946	C₂²	1	2	yes	—
13	#16863930	C₂²	1	1	yes	characteristic
14	#16863801	C₂²	1	1	yes	characteristic
15	#16863773	C₂²	1	1	yes	characteristic
16	#16863743	C₂²	1	2	yes	—
17	#16863697	—	2	2	no	—
18	#16863692	C₂²	1	2	yes	—
19	#16863687	C₂²	1	2	yes	—
20	#16863632	—	2	2	no	—
21	#16863632	—	2	1	no	—
22	#16863632	—	2	1	no	—
23	#16863625	—	2	2	no	—
24	#16863612	—	2	2	no	—
25	#16863597	C₂²	1	2	yes	—
26	#16863592	C₂²	1	2	yes	—
27	#16863526	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
29	C₄×D₅₃₆	—	2	1	no	—
30	C₄×D₅₃₆	—	2	1	no	—
31	#16863475	C₂²	1	1	yes	characteristic
32	#16863467	—	2	1	no	—
33	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₆₇	—	2	1	no	—
35	#16863455	—	2	1	no	—
36	#16863453	C₂²	1	1	yes	characteristic
37	#16863350	—	2	1	no	—
38	#16863144	C₂²	1	2	yes	—
39	#16863144	C₂²	1	2	yes	—
40	#16863139	C₂²	1	2	yes	—
41	#16863139	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#334×C₆₇	C₂²	1	2	yes	—
45	#334×C₆₇	C₂²	1	1	yes	characteristic
46	#334×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	—	2	2	no	—
48	C₂×#11761617	—	2	2	no	—
49	C₂×D₅₃₆	—	2	2	no	—
50	C₂×D₅₃₆	—	2	1	no	—
51	C₂×D₅₃₆	—	2	1	no	—
52	C₂×#11761611	—	2	1	no	—
53	C₂×C₈×D₆₇	—	2	1	no	—
54	#14524043	C₂³	1	2	yes	—
55	#14524040	C₂³	1	2	yes	—
56	#14524037	—	2	1	no	—
57	#14524035	D₄	1	1	yes	characteristic
58	#14524031	—	2	2	no	—
59	#14524031	D₄	1	1	yes	characteristic
60	#14524026	—	2	1	no	—
61	#14524022	D₄	1	1	yes	characteristic
62	#14524017	—	2	2	no	—
63	#14524017	—	2	2	no	—
64	#14524017	D₄	1	1	yes	characteristic
65	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
66	C₄×D₂₆₈	—	2	2	no	—
67	C₄×D₂₆₈	—	2	2	no	—
68	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₆₇	—	2	1	no	—
70	#14524000	—	2	1	no	—
71	#14523977	—	2	2	no	—
72	#14523977	—	2	1	no	—
73	#14523977	—	2	1	no	—
74	#14523975	—	2	2	no	—
75	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₆₇⋊C₈	—	2	1	no	—
78	Dic₆₇⋊C₈	—	2	1	no	—
79	#14523968	—	2	2	no	—
80	#14523965	—	2	2	no	—
81	#14523965	—	2	2	no	—
82	#14523965	—	2	2	no	—
83	#14523965	—	2	2	no	—
84	#14523965	—	2	2	no	—
85	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
86	(C₂×D₆₇)⋊C₈	—	2	1	no	—
87	(C₂×D₆₇)⋊C₈	—	2	1	no	—
88	#14523954	—	2	1	no	—
89	#14523953	—	2	1	no	—
90	C₈×Dic₆₇	—	2	1	no	—
91	C₂²×C₈×C₆₇	—	2	2	no	—
92	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₆₇	—	2	2	no	—
96	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
97	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
98	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	#11761628	—	8	4	no	—
103	C₂×Dic₁₃₄	—	2	2	no	—
104	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
105	C₂×D₂₆₈	—	2	2	no	—
106	C₂×D₂₆₈	—	2	2	no	—
107	C₂×D₂₆₈	—	2	2	no	—
108	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₆₇	—	2	1	no	—
110	C₂×C₂²⋊D₆₇	—	4	2	no	—
111	C₂×C₄×D₆₇	—	2	1	no	—
112	C₂×C₄×D₆₇	—	4	2	no	—
113	#11761617	—	8	2	no	—
114	D₅₃₆	—	4	2	no	—
115	D₅₃₆	—	4	2	no	—
116	D₅₃₆	—	8	2	no	—
117	#11761611	—	4	2	no	—
118	C₂×C₆₇⋊C₈	—	2	1	no	—
119	C₂×C₆₇⋊C₈	—	2	1	no	—
120	C₈×D₆₇	—	4	2	no	—
121	C₄⋊Dic₆₇	—	2	2	no	—
122	C₄⋊Dic₆₇	—	2	2	no	—
123	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
124	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
125	Dic₆₇⋊C₄	—	2	1	no	—
126	Dic₆₇⋊C₄	—	2	1	no	—
127	Dic₆₇⋊C₄	—	2	1	no	—
128	Dic₆₇⋊C₄	—	2	1	no	—
129	C₂²⋊Dic₆₇	—	2	1	no	—
130	(C₂×D₆₇)⋊C₄	—	2	1	no	—
131	(C₂×D₆₇)⋊C₄	—	2	1	no	—
132	(C₂×D₆₇)⋊C₄	—	2	1	no	—
133	(C₂×D₆₇)⋊C₄	—	2	1	no	—
134	(C₂×D₆₇)⋊C₄	—	4	2	no	—
135	(C₂×D₆₇)⋊C₄	—	4	2	no	—
136	C₄×Dic₆₇	—	2	1	no	—
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
140	C₂×C₈×C₆₇	—	2	2	no	—
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	—	2	2	no	—
143	C₂×C₈×C₆₇	—	4	1	no	—
144	C₂×C₈×C₆₇	—	8	2	no	—
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₇	#41	1	1	yes	characteristic
152	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
153	C₂³×C₆₇	#121	1	1	yes	characteristic
154	C₂²×D₆₇	—	2	1	no	—
155	C₂²×D₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
166	C₂²⋊D₆₇	—	4	2	no	—
167	C₂²⋊D₆₇	—	8	4	no	—
168	C₂×Dic₆₇	—	2	1	no	—
169	C₂×Dic₆₇	—	2	1	no	—
170	C₂×Dic₆₇	—	2	1	no	—
171	C₂×Dic₆₇	—	4	2	no	—
172	D₂₆₈	—	2	2	no	—
173	D₂₆₈	—	4	2	no	—
174	D₂₆₈	—	4	2	no	—
175	D₂₆₈	—	4	2	no	—
176	D₂₆₈	—	4	2	no	—
177	D₂₆₈	—	8	2	no	—
178	C₄×D₆₇	—	4	1	no	—
179	C₄×D₆₇	—	4	1	no	—
180	C₄×D₆₇	—	8	4	no	—
181	Dic₁₃₄	—	2	2	no	—
182	Dic₁₃₄	—	8	2	no	—
183	C₈×C₆₇	—	2	1	no	—
184	C₈×C₆₇	—	2	1	no	—
185	C₈×C₆₇	—	2	1	no	—
186	C₈×C₆₇	—	4	2	no	—
187	C₈×C₆₇	—	4	2	no	—
188	C₈×C₆₇	#135	1	2	yes	—
189	C₆₇⋊C₈	—	4	1	no	—
190	C₆₇⋊C₈	—	4	1	no	—
191	C₂²×C₆₇	—	2	1	no	—
192	C₂²×C₆₇	—	2	1	no	—
193	C₂²×C₆₇	#472	1	2	yes	—
194	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
195	C₂×D₆₇	—	4	1	no	—
196	C₂×D₆₇	—	4	1	no	—
197	C₂×D₆₇	—	4	1	no	—
198	C₂×D₆₇	—	8	2	no	—
199	C₂×D₆₇	—	8	2	no	—
200	C₂×D₆₇	—	8	2	no	—
201	C₄×C₆₇	—	2	1	no	—
202	C₄×C₆₇	—	2	1	no	—
203	C₄×C₆₇	—	2	1	no	—
204	C₄×C₆₇	—	2	1	no	—
205	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
206	C₄×C₆₇	#575	1	1	yes	characteristic
207	C₄×C₆₇	#577	1	2	yes	—
208	Dic₆₇	—	4	1	no	—
209	Dic₆₇	—	4	1	no	—
210	Dic₆₇	—	4	1	no	—
211	Dic₆₇	—	8	2	no	—
212	#19227	—	67	1	no	maximal, Sylow
213	C₂×C₆₇	—	2	2	no	—
214	C₂×C₆₇	#3035	1	1	yes	characteristic
215	C₂×C₆₇	#3060	1	1	yes	characteristic
216	C₂×C₆₇	C₂×#472	1	1	yes	characteristic
217	D₆₇	—	8	1	no	—
218	D₆₇	—	16	2	no	—
219	#3247	—	67	2	no	—
220	#3169	—	67	1	no	—
221	#2966	—	67	1	no	—
222	#1696	—	67	1	no	—
223	#1695	—	67	1	no	—
224	#1688	—	67	1	no	—
225	#1687	—	67	1	no	—
226	#1678	—	67	2	no	—
227	#1677	—	67	2	no	—
228	C₂×#334	D₆₇	1	1	yes	characteristic, complemented
229	#1551	—	67	2	no	—
230	C₆₇	#19227	1	1	yes	characteristic, complemented, Sylow
231	#532	—	67	2	no	—
232	#529	—	67	1	no	—
233	#500	—	67	1	no	—
234	#493	—	67	1	no	—
235	#486	—	67	2	no	—
236	#478	—	134	2	no	—
237	#477	—	67	2	no	—
238	#476	—	67	2	no	—
239	#466	—	134	2	no	—
240	#466	—	134	1	no	—
241	#466	—	134	1	no	—
242	#465	—	134	2	no	—
243	#463	—	134	2	no	—
244	#460	—	67	2	no	—
245	#459	—	67	2	no	—
246	#446	—	67	1	no	—
247	C₈×Q₈	—	67	1	no	—
248	C₄×D₈	—	134	1	no	—
249	C₄×D₈	—	134	1	no	—
250	#436	—	67	1	no	—
251	#435	—	134	1	no	—
252	C₈×D₄	—	67	1	no	—
253	C₈×D₄	—	134	1	no	—
254	#433	—	134	1	no	—
255	#432	—	67	1	no	—
256	C₂×C₄⋊C₈	C₂×D₆₇	1	2	yes	—
257	#405	—	134	1	no	—
258	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
259	#334	C₂×D₆₇	1	2	yes	—
260	#334	C₂×D₆₇	1	1	yes	characteristic
261	#334	C₂×D₆₇	1	1	yes	characteristic
262	#333	—	67	2	no	—
263	#333	—	67	2	no	—
264	#331	—	67	2	no	—
265	#331	—	67	2	no	—
266	C₂×#41	—	134	2	no	—
267	C₂×SD₁₆	—	134	2	no	—
268	C₂×D₈	—	134	2	no	—
269	C₂×D₈	—	134	1	no	—
270	C₂×D₈	—	134	1	no	—
271	C₂×M₁₆	—	134	1	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	134	1	no	—
274	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
275	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
276	C₄⋊Q₈	—	67	2	no	—
277	#127	—	67	2	no	—
278	#126	—	134	1	no	—
279	#125	—	67	1	no	—
280	#124	—	67	1	no	—
281	#124	—	134	2	no	—
282	#123	—	134	1	no	—
283	C₂²⋊Q₈	—	67	1	no	—
284	#121	—	67	1	no	—
285	#121	—	134	2	no	—
286	#121	—	134	2	no	—
287	C₄×Q₈	—	67	1	no	—
288	C₄×D₄	—	67	1	no	—
289	C₄×D₄	—	134	1	no	—
290	C₄×D₄	—	134	2	no	—
291	C₄×D₄	—	134	2	no	—
292	#117	—	134	1	no	—
293	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
294	#107	—	134	2	no	—
295	#107	—	134	1	no	—
296	#107	—	134	1	no	—
297	#106	—	134	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	67	1	no	—
300	C₄⋊C₈	—	67	1	no	—
301	C₄⋊C₈	—	134	1	no	—
302	C₄⋊C₈	—	134	1	no	—
303	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
304	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
305	#103	—	134	2	no	—
306	#102	—	134	2	no	—
307	#102	—	134	2	no	—
308	#102	—	134	2	no	—
309	#102	—	134	2	no	—
310	#102	—	134	2	no	—
311	C₂²⋊C₈	—	134	1	no	—
312	C₂²⋊C₈	—	134	1	no	—
313	C₂²⋊C₈	—	134	1	no	—
314	#97	—	134	1	no	—
315	#97	—	134	1	no	—
316	C₄×C₈	—	134	1	no	—
317	C₄×C₈	D₂₆₈	1	1	yes	characteristic
318	C₄×C₈	D₂₆₈	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
321	#41	—	536	4	no	—
322	C₂×Q₈	—	67	1	no	—
323	C₂×Q₈	—	134	2	no	—
324	C₂×D₄	—	268	2	no	—
325	C₂×D₄	—	67	1	no	—
326	C₂×D₄	—	134	1	no	—
327	C₂×D₄	—	134	2	no	—
328	C₂×D₄	—	134	2	no	—
329	C₂×D₄	—	134	2	no	—
330	C₂²×C₄	—	268	2	no	—
331	C₂²×C₄	—	134	1	no	—
332	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
334	C₂²×C₄	#11761629	1	1	yes	characteristic
335	SD₁₆	—	536	2	no	—
336	D₈	—	268	2	no	—
337	D₈	—	268	2	no	—
338	D₈	—	536	2	no	—
339	M₁₆	—	268	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	8	2	no	—
345	C₂×C₈	—	268	2	no	—
346	C₂×C₈	—	134	1	no	—
347	C₂×C₈	—	134	1	no	—
348	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
349	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
350	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
351	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
352	C₄⋊C₄	—	67	1	no	—
353	C₄⋊C₄	—	67	1	no	—
354	C₄⋊C₄	—	134	2	no	—
355	C₄⋊C₄	—	134	2	no	—
356	C₄⋊C₄	—	134	1	no	—
357	C₄⋊C₄	—	134	1	no	—
358	C₄⋊C₄	—	134	1	no	—
359	C₄⋊C₄	—	134	1	no	—
360	C₂²⋊C₄	—	268	2	no	—
361	C₂²⋊C₄	—	268	2	no	—
362	C₂²⋊C₄	—	134	1	no	—
363	C₂²⋊C₄	—	134	1	no	—
364	C₂²⋊C₄	—	134	1	no	—
365	C₂²⋊C₄	—	134	1	no	—
366	C₂²⋊C₄	—	134	1	no	—
367	C₄²	—	134	1	no	—
368	C₄²	D₄×D₆₇	1	1	yes	characteristic
369	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
370	C₄²	#11761629	1	1	yes	characteristic
371	C₄²	C₂³×D₆₇	1	1	yes	characteristic
372	C₂³	—	268	2	no	—
373	C₂³	—	134	1	no	—
374	C₂³	#14524018	1	1	yes	characteristic
375	Q₈	—	536	2	no	—
376	Q₈	—	134	2	no	—
377	D₄	—	268	2	no	—
378	D₄	—	268	2	no	—
379	D₄	—	268	2	no	—
380	D₄	—	268	2	no	—
381	D₄	—	268	2	no	—
382	D₄	—	536	2	no	—
383	D₄	—	536	4	no	—
384	D₄	—	134	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	268	1	no	—
390	C₂×C₄	—	268	1	no	—
391	C₂×C₄	—	268	2	no	—
392	C₂×C₄	—	536	4	no	—
393	C₂×C₄	—	134	1	no	—
394	C₂×C₄	—	134	1	no	—
395	C₂×C₄	—	134	1	no	—
396	C₂×C₄	#14524018	1	1	yes	characteristic
397	C₂×C₄	#14524018	1	1	yes	characteristic
398	C₂×C₄	#14524018	1	1	yes	characteristic
399	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
401	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	268	1	no	—
408	C₈	—	268	1	no	—
409	C₈	#14524065	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	268	1	no	—
413	C₂²	—	268	1	no	—
414	C₂²	—	268	1	no	—
415	C₂²	—	536	2	no	—
416	C₂²	—	536	2	no	—
417	C₂²	—	536	2	no	—
418	C₂²	#16863667	1	2	yes	—
419	C₂²	C₂×#14524018	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	268	1	no	—
425	C₄	—	268	1	no	—
426	C₄	—	268	1	no	—
427	C₄	—	536	2	no	—
428	C₄	C₂×#14524065	1	1	yes	characteristic
429	C₄	#16864196	1	1	yes	characteristic
430	C₄	#16864202	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	536	1	no	—
433	C₂	—	1072	2	no	—
434	C₂	#22569666	1	1	yes	characteristic
435	C₂	#22569872	1	1	yes	characteristic
436	C₂	C₂×#16863667	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524018
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#334×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	C₂×#334	D₆₇
hypocenter	C₆₇	#19227
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
1. #22571536	C₂	semidirect
2. #22570788	C₂	semidirect
3. #22569184	C₂	semidirect
4. #22559738	C₂	semidirect
5. #22559733	C₂	semidirect
6. #22559694	C₂	semidirect
7. #22559689	C₂	semidirect
8. #22559626	C₂	semidirect
9. #22559619	C₂	semidirect
10. #22558902	C₂	semidirect
11. C₂×#334×C₆₇	C₂	semidirect
228. C₂×#334	D₆₇	semidirect
230. C₆₇	#19227	semidirect

Maximal subgroups

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

subgroup	index
#22571536	2
#22570788	2
#22569184	2
#22559738	2
#22559733	2
#22559694	2
#22559689	2
#22559626	2
#22559619	2
#22558902	2
C₂×#334×C₆₇	2
#19227	67