Subgroups — #30839029

Order 17152.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22571350	C₂	1	1	yes	maximal, characteristic, complemented
2	#22571147	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863769	C₂	1	1	yes	maximal, characteristic
4	#22559681	C₂	1	4	yes	maximal, complemented
5	#22559557	C₂	1	4	yes	maximal, complemented
6	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558882	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558878	C₂	1	1	yes	maximal, characteristic
9	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#11761617	—	2	1	no	—
11	C₂²×#11761617	—	2	1	no	—
12	C₂×#14524043	C₂²	1	1	yes	characteristic
13	C₂×#14524040	C₂²	1	1	yes	characteristic
14	#16863792	—	2	1	no	—
15	#16863770	—	2	1	no	—
16	#16863769	—	2	1	no	—
17	#16863769	—	2	1	no	—
18	#16863769	C₂²	1	2	yes	—
19	#16863769	C₂²	1	2	yes	—
20	#16863746	—	2	1	no	—
21	#16863744	—	2	1	no	—
22	#16863724	—	2	2	no	—
23	#16863681	C₂²	1	4	yes	complemented
24	#16863596	C₂²	1	4	yes	—
25	#16863546	—	2	2	no	—
26	#16863449	C₂²	1	1	yes	characteristic
27	#16863449	C₂²	1	1	yes	characteristic
28	#16863149	C₂²	1	2	yes	complemented
29	#16863147	C₂²	1	2	yes	complemented
30	#16863143	C₂²	1	4	yes	complemented
31	#16863139	C₂²	1	4	yes	—
32	#533×C₆₇	C₂²	1	1	yes	characteristic
33	#446×C₆₇	—	2	1	no	—
34	#446×C₆₇	C₂²	1	2	yes	complemented
35	C₈×Q₈×C₆₇	—	2	1	no	—
36	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
37	#424×C₆₇	—	2	1	no	—
38	#423×C₆₇	C₂²	1	1	yes	characteristic
39	#405×C₆₇	—	2	1	no	—
40	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×Dic₁₃₄	—	2	1	no	—
42	C₂²×D₂₆₈	—	2	1	no	—
43	C₂²×D₂₆₈	—	2	1	no	—
44	C₂²×D₂₆₈	—	2	1	no	—
45	C₂×#11761617	—	2	2	no	—
46	C₂×#11761617	—	2	2	no	—
47	C₂×#11761617	—	2	2	no	—
48	C₂×#11761617	—	2	2	no	—
49	C₂×#11761617	—	4	4	no	—
50	C₂×#11761617	—	4	4	no	—
51	C₂×#11761615	—	2	4	no	—
52	#14524043	—	2	1	no	—
53	#14524043	—	2	1	no	—
54	#14524043	—	2	1	no	—
55	#14524043	C₂³	1	2	yes	—
56	#14524040	—	2	1	no	—
57	#14524040	—	2	1	no	—
58	#14524040	—	2	1	no	—
59	#14524040	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₆₇	—	2	1	no	—
61	C₂×C₄⋊Dic₆₇	—	2	1	no	—
62	#14523974	—	2	4	no	—
63	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
65	#14523967	—	2	4	no	—
66	#14523963	—	2	4	no	—
67	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
69	C₄×C₆₇⋊C₈	—	2	1	no	—
70	C₄×C₆₇⋊C₈	—	2	1	no	—
71	C₂×M₁₆×C₆₇	—	2	1	no	—
72	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
76	#125×C₆₇	—	2	1	no	—
77	C₂²⋊Q₈×C₆₇	—	2	1	no	—
78	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
79	C₄×Q₈×C₆₇	—	2	1	no	—
80	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
81	#117×C₆₇	—	2	1	no	—
82	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₆₇	—	2	2	no	—
84	C₄⋊C₈×C₆₇	—	2	2	no	—
85	C₄⋊C₈×C₆₇	—	2	1	no	—
86	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
87	#97×C₆₇	—	2	2	no	—
88	C₄×C₈×C₆₇	—	2	2	no	—
89	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
90	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×D₆₇	—	4	1	no	—
94	C₂×Dic₁₃₄	—	2	2	no	—
95	C₂×Dic₁₃₄	—	4	2	no	—
96	C₂×Dic₁₃₄	—	4	2	no	—
97	C₂×Dic₁₃₄	—	4	1	no	—
98	C₂×D₂₆₈	—	2	2	no	—
99	C₂×D₂₆₈	—	2	2	no	—
100	C₂×D₂₆₈	—	2	2	no	—
101	C₂×D₂₆₈	—	4	2	no	—
102	C₂×D₂₆₈	—	4	2	no	—
103	C₂×D₂₆₈	—	4	1	no	—
104	C₂×D₂₆₈	—	4	1	no	—
105	C₂×D₂₆₈	—	4	1	no	—
106	C₂×D₂₆₈	—	8	2	no	—
107	C₂×D₂₆₈	—	8	2	no	—
108	C₂²×Dic₆₇	—	4	1	no	—
109	#11761617	—	4	4	no	—
110	#11761617	—	4	4	no	—
111	#11761617	—	4	4	no	—
112	#11761617	—	4	4	no	—
113	#11761615	—	8	4	no	—
114	C₂×C₆₇⋊C₈	—	2	2	no	—
115	C₂×C₆₇⋊C₈	—	2	2	no	—
116	C₄⋊Dic₆₇	—	2	2	no	—
117	C₄⋊Dic₆₇	—	2	2	no	—
118	C₄⋊Dic₆₇	—	4	1	no	—
119	C₄⋊Dic₆₇	—	4	1	no	—
120	C₂×Q₈×C₆₇	—	2	1	no	—
121	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
125	M₁₆×C₆₇	—	4	2	no	—
126	C₂×C₈×C₆₇	—	2	2	no	—
127	C₂×C₈×C₆₇	—	2	2	no	—
128	C₂×C₈×C₆₇	SD₁₆	1	4	yes	complemented
129	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₆₇	—	2	1	no	—
134	C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₄⋊C₄×C₆₇	—	2	2	no	—
137	C₄⋊C₄×C₆₇	—	2	2	no	—
138	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₆₇	—	2	2	no	—
140	C₄²×C₆₇	—	2	2	no	—
141	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₆₇	#41	1	1	yes	characteristic
144	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₆₇	#121	1	1	yes	characteristic
146	C₂²×D₆₇	—	4	2	no	—
147	C₂²×D₆₇	—	8	2	no	—
148	C₂²×D₆₇	—	8	2	no	—
149	C₂²×D₆₇	—	8	2	no	—
150	Q₈×C₆₇	—	2	4	no	—
151	Q₈×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	2	2	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₆₇	—	4	2	no	—
165	C₂×Dic₆₇	—	8	2	no	—
166	D₂₆₈	—	4	2	no	—
167	D₂₆₈	—	4	2	no	—
168	D₂₆₈	—	4	4	no	—
169	D₂₆₈	—	8	2	no	—
170	D₂₆₈	—	8	2	no	—
171	D₂₆₈	—	8	2	no	—
172	D₂₆₈	—	8	2	no	—
173	Dic₁₃₄	—	4	2	no	—
174	Dic₁₃₄	—	4	2	no	—
175	Dic₁₃₄	—	8	2	no	—
176	C₈×C₆₇	—	2	1	no	—
177	C₈×C₆₇	—	2	1	no	—
178	C₈×C₆₇	—	4	2	no	—
179	C₈×C₆₇	C₂×SD₁₆	1	2	yes	—
180	C₈×C₆₇	C₂×SD₁₆	1	2	yes	—
181	C₆₇⋊C₈	—	4	2	no	—
182	C₆₇⋊C₈	—	4	2	no	—
183	C₂²×C₆₇	—	2	1	no	—
184	C₂²×C₆₇	—	2	1	no	—
185	C₂²×C₆₇	#460	1	2	yes	—
186	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
187	C₂×D₆₇	—	8	2	no	—
188	C₂×D₆₇	—	8	2	no	—
189	C₂×D₆₇	—	8	2	no	—
190	C₂×D₆₇	—	16	4	no	—
191	C₄×C₆₇	—	2	1	no	—
192	C₄×C₆₇	—	2	1	no	—
193	C₄×C₆₇	—	4	2	no	—
194	C₄×C₆₇	—	4	2	no	—
195	C₄×C₆₇	#460	1	2	yes	—
196	C₄×C₆₇	#471	1	2	yes	—
197	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
198	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₆₇	#577	1	2	yes	—
200	Dic₆₇	—	8	2	no	—
201	#19202	—	67	1	no	maximal, Sylow
202	C₂×C₆₇	—	2	2	no	—
203	C₂×C₆₇	C₂×#460	1	1	yes	characteristic
204	C₂×C₆₇	#3057	1	1	yes	characteristic
205	C₂×C₆₇	C₂×#471	1	1	yes	characteristic
206	D₆₇	—	16	2	no	—
207	#3229	—	67	1	no	—
208	#3208	—	67	1	no	—
209	C₂×#492	—	67	1	no	—
210	#2960	D₆₇	1	1	yes	characteristic, complemented
211	#1686	—	67	4	no	—
212	#1666	—	67	4	no	—
213	#1564	—	67	1	no	—
214	#1546	—	67	1	no	—
215	#1545	—	67	1	no	—
216	C₆₇	#19202	1	1	yes	characteristic, complemented, Sylow
217	C₂²×SD₁₆	—	134	1	no	—
218	C₂²×SD₁₆	—	134	1	no	—
219	#533	C₂×D₆₇	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	—	67	1	no	—
221	C₂×#127	—	67	1	no	—
222	#498	—	134	1	no	—
223	#492	—	67	2	no	—
224	#492	—	67	2	no	—
225	#492	—	134	1	no	—
226	#492	—	134	1	no	—
227	#492	—	134	1	no	—
228	#487	—	134	1	no	—
229	#486	—	134	1	no	—
230	#483	—	134	2	no	—
231	#475	—	67	4	no	—
232	#460	—	67	4	no	—
233	#450	—	134	2	no	—
234	#446	—	2	1	no	—
235	#446	C₂×D₆₇	1	2	yes	complemented
236	C₈×Q₈	—	2	1	no	—
237	C₈×Q₈	C₂×D₆₇	1	2	yes	complemented
238	#431	—	67	1	no	—
239	#431	—	67	1	no	—
240	#424	—	2	1	no	—
241	#423	C₂×D₆₇	1	1	yes	characteristic
242	#405	—	2	1	no	—
243	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
244	#335	—	67	2	no	—
245	#334	—	67	2	no	—
246	#332	—	67	4	no	—
247	#331	—	67	4	no	—
248	C₂²×Q₈	—	134	1	no	—
249	C₂²×D₄	—	134	1	no	—
250	C₂²×D₄	—	134	1	no	—
251	C₂²×D₄	—	134	1	no	—
252	C₂×SD₁₆	—	268	4	no	—
253	C₂×SD₁₆	—	268	4	no	—
254	C₂×SD₁₆	—	134	4	no	—
255	C₂×SD₁₆	—	134	2	no	—
256	C₂×SD₁₆	—	134	2	no	—
257	C₂×SD₁₆	—	134	2	no	—
258	C₂×SD₁₆	—	134	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
261	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
262	C₄⋊Q₈	—	67	2	no	—
263	C₄⋊Q₈	—	134	1	no	—
264	C₄⋊Q₈	—	134	1	no	—
265	C₄⋊Q₈	—	134	1	no	—
266	C₄⋊Q₈	D₂₆₈	1	1	yes	characteristic
267	C₄⋊Q₈	D₂₆₈	1	1	yes	characteristic
268	#127	—	67	2	no	—
269	#127	—	134	1	no	—
270	#127	—	134	1	no	—
271	#127	—	134	1	no	—
272	#125	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	D₂₆₈	1	2	yes	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
277	#117	—	2	1	no	—
278	C₂×C₄⋊C₄	—	134	1	no	—
279	C₂×C₄⋊C₄	—	134	1	no	—
280	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
281	#106	—	134	4	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	67	2	no	—
286	C₄⋊C₈	—	67	2	no	—
287	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
288	#103	—	134	4	no	—
289	#102	—	134	4	no	—
290	C₂²⋊C₈	—	134	1	no	—
291	C₂²⋊C₈	—	134	1	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	134	1	no	—
295	C₄×C₈	—	134	1	no	—
296	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
297	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
300	C₂⁴	—	268	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	268	1	no	—
303	C₂×Q₈	—	268	2	no	—
304	C₂×Q₈	—	268	2	no	—
305	C₂×Q₈	—	134	2	no	—
306	C₂×Q₈	C₂×D₂₆₈	1	2	yes	—
307	C₂×D₄	—	268	1	no	—
308	C₂×D₄	—	268	1	no	—
309	C₂×D₄	—	268	1	no	—
310	C₂×D₄	—	268	2	no	—
311	C₂×D₄	—	268	2	no	—
312	C₂×D₄	—	536	2	no	—
313	C₂×D₄	—	536	2	no	—
314	C₂×D₄	—	134	2	no	—
315	C₂×D₄	—	134	2	no	—
316	C₂×D₄	—	134	2	no	—
317	C₂²×C₄	—	268	1	no	—
318	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
320	C₂²×C₄	#11761628	1	1	yes	characteristic
321	SD₁₆	—	268	4	no	—
322	SD₁₆	—	268	4	no	—
323	SD₁₆	—	268	4	no	—
324	SD₁₆	—	268	4	no	—
325	SD₁₆	—	536	4	no	—
326	M₁₆	—	4	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	134	2	no	—
330	C₂×C₈	—	134	2	no	—
331	C₂×C₈	#11761615	1	4	yes	complemented
332	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
335	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	268	1	no	—
342	C₄⋊C₄	—	268	1	no	—
343	C₄⋊C₄	—	134	2	no	—
344	C₄⋊C₄	—	134	2	no	—
345	C₄⋊C₄	C₂×D₂₆₈	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
349	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
350	C₄²	#11761628	1	1	yes	characteristic
351	C₄²	C₂³×D₆₇	1	1	yes	characteristic
352	C₂³	—	268	2	no	—
353	C₂³	—	536	2	no	—
354	C₂³	—	536	2	no	—
355	C₂³	—	536	2	no	—
356	C₂³	#14524017	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	268	2	no	—
360	Q₈	—	268	2	no	—
361	Q₈	—	536	2	no	—
362	D₄	—	268	2	no	—
363	D₄	—	268	2	no	—
364	D₄	—	268	4	no	—
365	D₄	—	536	2	no	—
366	D₄	—	536	2	no	—
367	D₄	—	536	2	no	—
368	D₄	—	536	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	268	2	no	—
374	C₂×C₄	—	536	2	no	—
375	C₂×C₄	#14524017	1	1	yes	characteristic
376	C₂×C₄	#14524017	1	1	yes	characteristic
377	C₂×C₄	#14524017	1	1	yes	characteristic
378	C₂×C₄	C₂×#11761615	1	2	yes	—
379	C₂×C₄	#14524068	1	2	yes	—
380	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
382	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	4	2	no	—
386	C₈	—	268	2	no	—
387	C₈	—	268	2	no	—
388	C₈	C₂×#11761615	1	2	yes	—
389	C₈	C₂×#11761615	1	2	yes	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	536	2	no	—
393	C₂²	—	536	2	no	—
394	C₂²	—	536	2	no	—
395	C₂²	—	1072	4	no	—
396	C₂²	#16863596	1	2	yes	—
397	C₂²	C₂×#14524017	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	536	2	no	—
403	C₄	#16863596	1	2	yes	—
404	C₄	#16863659	1	2	yes	—
405	C₄	C₂²×#11761615	1	1	yes	characteristic
406	C₄	C₂×#14524068	1	1	yes	characteristic
407	C₄	#16864208	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	1072	2	no	—
410	C₂	C₂×#16863596	1	1	yes	characteristic
411	C₂	#22569848	1	1	yes	characteristic
412	C₂	C₂×#16863659	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524017
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2960	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	C₂×#14524040	C₂²
hypercenter	#2960	D₆₇
hypocenter	C₆₇	#19202
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

Complements

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

N	H ≅ G/N	type
1. #22571350	C₂	semidirect
4. #22559681	C₂	semidirect
5. #22559557	C₂	semidirect
6. #22558957	C₂	semidirect
7. #22558882	C₂	semidirect
9. C₆₇×#2960	C₂	semidirect
23. #16863681	C₂²	semidirect
28. #16863149	C₂²	semidirect
29. #16863147	C₂²	semidirect
30. #16863143	C₂²	semidirect
34. #446×C₆₇	C₂²	semidirect
36. C₈×Q₈×C₆₇	C₂²	semidirect
128. C₂×C₈×C₆₇	SD₁₆	semidirect
210. #2960	D₆₇	semidirect
216. C₆₇	#19202	semidirect
235. #446	C₂×D₆₇	semidirect
237. C₈×Q₈	C₂×D₆₇	semidirect
331. C₂×C₈	#11761615	semidirect

Maximal subgroups

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

subgroup	index
#22571350	2
#22571147	2
C₂×#16863769	2
#22559681	2
#22559557	2
#22558957	2
#22558882	2
#22558878	2
C₆₇×#2960	2
#19202	67