Subgroups — #30874834

Order 17152.

642 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic
2	#22569160	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863520	C₂	1	1	yes	maximal, characteristic
4	#22560985	C₂	1	1	yes	maximal, characteristic
5	#22560983	C₂	1	2	yes	maximal
6	#22560981	C₂	1	2	yes	maximal
7	#22560346	C₂	1	1	yes	maximal, characteristic
8	#22560345	C₂	1	2	yes	maximal
9	#108×Dic₆₇	C₂	1	2	yes	maximal
10	C₄×#14523978	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#1950	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
13	#16863526	—	2	1	no	—
14	#16863525	—	2	2	no	—
15	#16863524	—	2	2	no	—
16	#16863523	—	2	1	no	—
17	C₈×Dic₁₃₄	—	2	1	no	—
18	#16863520	—	2	1	no	—
19	#16863520	C₄	1	4	yes	—
20	#16863520	C₄	1	2	yes	—
21	#16863520	C₄	1	2	yes	—
22	C₂×#14523979	C₂²	1	2	yes	—
23	C₂×#14523978	C₂²	1	1	yes	characteristic
24	C₂×#14523978	C₂²	1	1	yes	characteristic
25	#16863420	C₂²	1	1	yes	characteristic
26	#16863419	C₂²	1	2	yes	—
27	#16863419	C₂²	1	2	yes	—
28	C₂×Dic₆₇⋊C₈	C₂²	1	2	yes	—
29	C₄×#11761612	C₂²	1	1	yes	characteristic
30	M₁₆×Dic₆₇	C₂²	1	2	yes	—
31	M₁₆×Dic₆₇	C₂²	1	2	yes	—
32	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₆₇	C₂²	1	2	yes	—
34	#16863161	C₂²	1	2	yes	—
35	#16863160	C₂²	1	1	yes	characteristic
36	#16863160	C₂²	1	2	yes	—
37	#16863160	C₂²	1	2	yes	—
38	#16863160	C₂²	1	1	yes	characteristic
39	C₂×#108×C₆₇	C₂²	1	2	yes	—
40	#423×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
43	#341×C₆₇	C₂²	1	2	yes	—
44	C₂²×Dic₁₃₄	Q₈	1	1	yes	characteristic
45	C₂×#11761612	C₂³	1	2	yes	—
46	C₂×#11761612	C₂³	1	1	yes	characteristic
47	C₂×#11761612	C₂³	1	1	yes	characteristic
48	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
51	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
52	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
54	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
55	C₄×Dic₁₃₄	D₄	1	2	yes	—
56	C₂×C₄⋊Dic₆₇	Q₈	1	1	yes	characteristic
57	C₂×Dic₆₇⋊C₄	Q₈	1	2	yes	—
58	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
59	#14523979	—	2	4	no	—
60	#14523978	—	2	2	no	—
61	#14523978	—	2	2	no	—
62	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
64	Dic₆₇⋊C₈	—	2	2	no	—
65	Dic₆₇⋊C₈	—	2	2	no	—
66	Dic₆₇⋊C₈	—	2	2	no	—
67	Dic₆₇⋊C₈	—	2	2	no	—
68	Dic₆₇⋊C₈	C₂×C₄	1	4	yes	—
69	Dic₆₇⋊C₈	C₂×C₄	1	4	yes	—
70	#14523954	—	2	1	no	—
71	#14523953	—	2	2	no	—
72	#14523953	—	2	2	no	—
73	C₄×C₆₇⋊C₈	—	2	1	no	—
74	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
75	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
76	C₈×Dic₆₇	—	2	2	no	—
77	C₈×Dic₆₇	—	2	2	no	—
78	C₈×Dic₆₇	C₂×C₄	1	4	yes	—
79	C₈×Dic₆₇	C₂×C₄	1	4	yes	—
80	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
81	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
85	#108×C₆₇	—	2	4	no	—
86	C₄⋊C₈×C₆₇	—	2	1	no	—
87	C₄⋊C₈×C₆₇	—	2	1	no	—
88	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
89	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
90	#97×C₆₇	—	2	1	no	—
91	C₄×C₈×C₆₇	—	2	1	no	—
92	C₂×Dic₁₃₄	—	2	4	no	—
93	C₂×Dic₁₃₄	C₄⋊C₄	1	1	yes	characteristic
94	C₂×Dic₁₃₄	C₄⋊C₄	1	2	yes	—
95	C₂×Dic₁₃₄	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×Dic₆₇	C₂×Q₈	1	2	yes	—
97	C₂²×Dic₆₇	C₂×Q₈	1	2	yes	—
98	#11761612	—	2	1	no	—
99	#11761612	—	2	1	no	—
100	#11761612	—	2	2	no	—
101	#11761612	—	2	1	no	—
102	#11761612	—	2	2	no	—
103	#11761612	#41	1	2	yes	—
104	C₂×C₆₇⋊C₈	—	2	1	no	—
105	C₂×C₆₇⋊C₈	—	2	1	no	—
106	C₂×C₆₇⋊C₈	—	2	1	no	—
107	C₂×C₆₇⋊C₈	—	2	1	no	—
108	C₂×C₆₇⋊C₈	—	2	1	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₂×C₆₇⋊C₈	—	2	1	no	—
111	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
112	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
113	C₄⋊Dic₆₇	C₄⋊C₄	1	2	yes	—
114	C₄⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
115	C₄⋊Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
116	Dic₆₇⋊C₄	C₄⋊C₄	1	2	yes	—
117	Dic₆₇⋊C₄	C₄⋊C₄	1	2	yes	—
118	Dic₆₇⋊C₄	C₄⋊C₄	1	2	yes	—
119	Dic₆₇⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
121	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
122	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
123	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₆₇	—	2	1	no	—
128	M₁₆×C₆₇	—	2	2	no	—
129	M₁₆×C₆₇	—	2	1	no	—
130	M₁₆×C₆₇	—	2	2	no	—
131	M₁₆×C₆₇	—	2	1	no	—
132	M₁₆×C₆₇	#41	1	2	yes	—
133	C₂×C₈×C₆₇	—	2	1	no	—
134	C₂×C₈×C₆₇	—	2	2	no	—
135	C₂×C₈×C₆₇	—	2	2	no	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	—	2	1	no	—
138	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
139	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	4	1	no	—
146	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
156	C₂×Dic₆₇	—	2	4	no	—
157	C₂×Dic₆₇	—	4	2	no	—
158	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×Dic₆₇	C₂×C₄⋊C₄	1	2	yes	—
162	Dic₁₃₄	—	2	2	no	—
163	Dic₁₃₄	—	2	4	no	—
164	Dic₁₃₄	#108	1	4	yes	complemented
165	C₈×C₆₇	—	2	4	no	—
166	C₈×C₆₇	—	2	2	no	—
167	C₈×C₆₇	—	4	2	no	—
168	C₈×C₆₇	—	4	1	no	—
169	C₆₇⋊C₈	—	2	2	no	—
170	C₆₇⋊C₈	—	2	2	no	—
171	C₆₇⋊C₈	—	2	2	no	—
172	C₆₇⋊C₈	—	4	1	no	—
173	C₆₇⋊C₈	—	4	2	no	—
174	C₂²×C₆₇	—	2	1	no	—
175	C₂²×C₆₇	—	2	1	no	—
176	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₆₇	#557	1	1	yes	characteristic
178	C₂²×C₆₇	#557	1	1	yes	characteristic
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	C₂×#108	1	2	yes	—
183	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
184	C₄×C₆₇	#519	1	1	yes	characteristic
185	C₄×C₆₇	#548	1	1	yes	characteristic
186	C₄×C₆₇	#548	1	1	yes	characteristic
187	Dic₆₇	—	2	2	no	—
188	Dic₆₇	—	2	2	no	—
189	Dic₆₇	—	2	2	no	—
190	Dic₆₇	C₂×#108	1	4	yes	—
191	#22746	—	67	1	no	maximal, Sylow
192	C₂×C₆₇	—	2	1	no	—
193	C₂×C₆₇	—	2	1	no	—
194	C₂×C₆₇	#2351	1	1	yes	characteristic
195	C₂×C₆₇	C₂²×#108	1	1	yes	characteristic
196	C₂×C₆₇	#2916	1	1	yes	characteristic
197	Q₈×M₁₆	—	67	1	no	—
198	Q₈×M₁₆	—	67	1	no	—
199	C₂×C₈×Q₈	—	67	1	no	—
200	#1950	—	67	2	no	—
201	#1950	—	67	1	no	—
202	#1950	—	67	2	no	—
203	#1950	D₆₇	1	1	yes	characteristic
204	#1837	—	67	1	no	—
205	#1837	—	67	2	no	—
206	C₄×#108	—	67	2	no	—
207	C₄×#108	—	67	1	no	—
208	C₆₇	#22746	1	1	yes	characteristic, complemented, Sylow
209	C₂×C₄×Q₈	—	67	1	no	—
210	#446	—	134	1	no	—
211	#446	—	134	2	no	—
212	#446	—	134	1	no	—
213	#446	—	134	2	no	—
214	C₈×Q₈	—	67	2	no	—
215	C₈×Q₈	—	67	4	no	—
216	C₈×Q₈	—	67	2	no	—
217	C₈×Q₈	—	134	1	no	—
218	C₈×Q₈	—	134	1	no	—
219	C₂×#108	—	67	1	no	—
220	C₂×#108	—	67	1	no	—
221	C₂×#108	—	67	2	no	—
222	C₂×#108	C₂×D₆₇	1	2	yes	—
223	#423	—	67	2	no	—
224	#423	—	67	2	no	—
225	#423	—	67	1	no	—
226	#423	C₂×D₆₇	1	1	yes	characteristic
227	C₂×C₄⋊C₈	—	67	2	no	—
228	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
229	C₄×M₁₆	—	67	2	no	—
230	C₄×M₁₆	—	67	2	no	—
231	C₄×M₁₆	—	67	1	no	—
232	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
233	C₂×C₄×C₈	—	67	2	no	—
234	C₂×C₄×C₈	—	67	1	no	—
235	#341	—	67	2	no	—
236	#341	—	67	1	no	—
237	#341	—	67	2	no	—
238	#341	—	67	1	no	—
239	#341	—	67	2	no	—
240	#341	C₂×D₆₇	1	2	yes	—
241	C₂²×Q₈	—	67	1	no	—
242	C₂×M₁₆	—	67	1	no	—
243	C₂×M₁₆	—	67	2	no	—
244	C₂×M₁₆	—	67	1	no	—
245	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
246	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
247	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
248	C₂²×C₈	—	67	1	no	—
249	C₂²×C₈	—	67	1	no	—
250	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
251	C₄×Q₈	—	67	1	no	—
252	C₄×Q₈	—	67	2	no	—
253	C₄×Q₈	—	67	1	no	—
254	C₄×Q₈	—	67	1	no	—
255	C₄×Q₈	—	67	2	no	—
256	C₄×Q₈	—	67	1	no	—
257	C₂×C₄⋊C₄	—	67	2	no	—
258	C₂×C₄⋊C₄	—	67	1	no	—
259	C₂×C₄²	—	67	2	no	—
260	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
261	#108	—	2	4	no	—
262	#108	—	134	4	no	—
263	#108	—	134	2	no	—
264	#108	—	134	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	67	4	no	—
268	C₄⋊C₈	—	67	4	no	—
269	C₄⋊C₈	—	134	2	no	—
270	C₄⋊C₈	—	134	2	no	—
271	C₄⋊C₈	—	134	2	no	—
272	C₄⋊C₈	—	134	2	no	—
273	C₄⋊C₈	—	134	1	no	—
274	C₄⋊C₈	—	134	1	no	—
275	C₄⋊C₈	C₄×D₆₇	1	2	yes	—
276	C₄⋊C₈	C₄×D₆₇	1	2	yes	—
277	#97	—	2	1	no	—
278	#97	—	134	2	no	—
279	#97	—	134	2	no	—
280	#97	—	134	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	67	4	no	—
283	C₄×C₈	—	67	4	no	—
284	C₄×C₈	—	67	2	no	—
285	C₄×C₈	—	67	2	no	—
286	C₄×C₈	—	134	2	no	—
287	C₄×C₈	—	134	2	no	—
288	C₄×C₈	—	134	1	no	—
289	C₂×Q₈	—	67	1	no	—
290	C₂×Q₈	—	67	2	no	—
291	C₂×Q₈	—	67	1	no	—
292	C₂×Q₈	—	134	4	no	—
293	C₂²×C₄	—	67	2	no	—
294	C₂²×C₄	—	67	2	no	—
295	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
296	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
297	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
298	M₁₆	—	2	1	no	—
299	M₁₆	—	2	1	no	—
300	M₁₆	—	2	2	no	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	2	1	no	—
303	M₁₆	—	67	2	no	—
304	M₁₆	—	134	2	no	—
305	M₁₆	—	134	1	no	—
306	M₁₆	—	134	1	no	—
307	M₁₆	—	134	2	no	—
308	M₁₆	—	134	1	no	—
309	M₁₆	#11761627	1	2	yes	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	67	2	no	—
316	C₂×C₈	—	67	2	no	—
317	C₂×C₈	—	134	1	no	—
318	C₂×C₈	—	134	2	no	—
319	C₂×C₈	—	134	1	no	—
320	C₂×C₈	—	134	1	no	—
321	C₂×C₈	—	134	1	no	—
322	C₂×C₈	—	134	1	no	—
323	C₂×C₈	—	134	1	no	—
324	C₂×C₈	C₂×C₄×D₆₇	1	4	yes	—
325	C₄⋊C₄	—	67	2	no	—
326	C₄⋊C₄	—	67	2	no	—
327	C₄⋊C₄	—	67	2	no	—
328	C₄⋊C₄	—	67	2	no	—
329	C₄⋊C₄	—	67	2	no	—
330	C₄⋊C₄	—	67	1	no	—
331	C₄⋊C₄	—	67	1	no	—
332	C₄²	—	67	2	no	—
333	C₄²	—	67	2	no	—
334	C₄²	—	67	2	no	—
335	C₄²	—	67	2	no	—
336	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
337	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
338	C₄²	D₄×D₆₇	1	1	yes	characteristic
339	C₄²	D₄×D₆₇	1	1	yes	characteristic
340	C₂³	C₂×Q₈×D₆₇	1	1	yes	characteristic
341	Q₈	—	67	4	no	—
342	Q₈	—	134	4	no	—
343	Q₈	—	134	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	268	2	no	—
347	C₂×C₄	—	67	2	no	—
348	C₂×C₄	—	67	2	no	—
349	C₂×C₄	—	67	2	no	—
350	C₂×C₄	—	67	2	no	—
351	C₂×C₄	—	134	4	no	—
352	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
353	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
354	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
355	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
357	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
358	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
360	C₂×C₄	#14524090	1	1	yes	characteristic
361	C₂×C₄	#14524091	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	2	4	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	1	no	—
366	C₈	—	268	1	no	—
367	C₈	—	268	2	no	—
368	C₈	—	134	2	no	—
369	C₈	—	134	2	no	—
370	C₈	—	134	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
374	C₂²	#16864121	1	1	yes	characteristic
375	C₂²	#16864123	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	67	4	no	—
380	C₄	—	134	2	no	—
381	C₄	—	134	2	no	—
382	C₄	—	134	2	no	—
383	C₄	#108×D₆₇	1	2	yes	—
384	C₄	C₄×#11761627	1	1	yes	characteristic
385	C₄	#16863872	1	1	yes	characteristic
386	C₄	#16864052	1	1	yes	characteristic
387	C₄	#16864056	1	1	yes	characteristic
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	#22563128	1	1	yes	characteristic
391	C₂	C₂×#108×D₆₇	1	1	yes	characteristic
392	C₂	#22568819	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1950	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂³×C₆₇	C₂²×Q₈
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1950	D₆₇
hypocenter	C₆₇	#22746
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
164. Dic₁₃₄	#108	semidirect
208. C₆₇	#22746	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×Dic₁₃₄	2
#22569160	2
C₂×#16863520	2
#22560985	2
#22560983	2
#22560981	2
#22560346	2
#22560345	2
#108×Dic₆₇	2
C₄×#14523978	2
C₆₇×#1950	2
#22746	67