Subgroups — #30751477

Order 17152.

644 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	#22560189	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863142	C₂	1	2	yes	maximal, complemented
4	#22558092	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2857	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₆₇⋊C₈	—	2	1	no	—
7	C₂×C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
8	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
9	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
12	#16863151	—	2	1	no	—
13	#16863142	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
16	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
17	#391×C₆₇	—	2	1	no	—
18	#389×C₆₇	—	2	1	no	—
19	#389×C₆₇	C₄	1	2	yes	—
20	#384×C₆₇	C₂²	1	1	yes	characteristic
21	#380×C₆₇	—	2	1	no	—
22	#380×C₆₇	C₄	1	2	yes	—
23	C₂²×C₆₇⋊C₈	—	2	4	no	—
24	C₂²×C₆₇⋊C₈	—	2	2	no	—
25	C₂²×C₆₇⋊C₈	—	2	2	no	—
26	C₂²×C₆₇⋊C₈	—	4	2	no	—
27	C₂²×C₆₇⋊C₈	—	4	2	no	—
28	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
29	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
31	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₆₇⋊C₈)	D₄	1	4	yes	—
33	C₂²⋊(C₆₇⋊C₈)	—	4	2	no	—
34	C₂²×Q₈×C₆₇	—	2	1	no	—
35	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
38	C₄⋊Q₈×C₆₇	—	2	2	no	—
39	C₄⋊Q₈×C₆₇	—	2	2	no	—
40	C₂²⋊Q₈×C₆₇	—	4	2	no	—
41	C₂²⋊Q₈×C₆₇	—	4	2	no	—
42	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
44	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
46	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
48	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
49	C₂×C₄²×C₆₇	—	2	2	no	—
50	C₂×C₄²×C₆₇	—	2	2	no	—
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
55	#95×C₆₇	—	2	2	no	—
56	#95×C₆₇	—	2	2	no	—
57	C₂×C₆₇⋊C₈	—	2	4	no	—
58	C₂×C₆₇⋊C₈	—	4	8	no	—
59	C₂×C₆₇⋊C₈	—	4	2	no	—
60	C₂×C₆₇⋊C₈	—	4	2	no	—
61	C₂×C₆₇⋊C₈	—	4	2	no	—
62	C₂×C₆₇⋊C₈	—	4	2	no	—
63	C₂×C₆₇⋊C₈	—	4	2	no	—
64	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×Q₈×C₆₇	—	4	2	no	—
66	C₂×Q₈×C₆₇	—	4	1	no	—
67	C₂×Q₈×C₆₇	—	4	1	no	—
68	C₂×Q₈×C₆₇	—	4	2	no	—
69	C₂²×C₄×C₆₇	—	2	1	no	—
70	C₂²×C₄×C₆₇	—	2	2	no	—
71	C₂²×C₄×C₆₇	—	2	1	no	—
72	C₂²×C₄×C₆₇	—	2	2	no	—
73	C₂²×C₄×C₆₇	—	2	1	no	—
74	C₂²×C₄×C₆₇	—	2	1	no	—
75	C₂²×C₄×C₆₇	—	2	2	no	—
76	C₂²×C₄×C₆₇	—	2	2	no	—
77	C₂²×C₄×C₆₇	—	2	2	no	—
78	C₂²×C₄×C₆₇	—	2	2	no	—
79	C₂²×C₄×C₆₇	—	4	1	no	—
80	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	D₈	1	2	yes	—
84	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₆₇	Q₁₆	1	2	yes	—
87	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
90	C₄⋊C₄×C₆₇	—	2	4	no	—
91	C₄⋊C₄×C₆₇	—	4	2	no	—
92	C₄⋊C₄×C₆₇	—	4	4	no	—
93	C₄⋊C₄×C₆₇	—	4	1	no	—
94	C₄⋊C₄×C₆₇	—	4	1	no	—
95	C₄⋊C₄×C₆₇	—	4	1	no	—
96	C₄⋊C₄×C₆₇	—	4	1	no	—
97	C₄⋊C₄×C₆₇	—	4	1	no	—
98	C₄⋊C₄×C₆₇	—	4	1	no	—
99	C₂²⋊C₄×C₆₇	—	4	4	no	—
100	C₄²×C₆₇	—	2	2	no	—
101	C₄²×C₆₇	—	2	1	no	—
102	C₄²×C₆₇	—	2	2	no	—
103	C₄²×C₆₇	—	2	1	no	—
104	C₄²×C₆₇	C₂×D₄	1	2	yes	—
105	C₄²×C₆₇	#41	1	2	yes	—
106	C₂³×C₆₇	—	2	1	no	—
107	C₂³×C₆₇	—	2	1	no	—
108	C₂³×C₆₇	—	2	1	no	—
109	C₂³×C₆₇	—	2	1	no	—
110	C₂³×C₆₇	#101	1	2	yes	—
111	C₂³×C₆₇	#102	1	2	yes	—
112	C₂³×C₆₇	#103	1	2	yes	—
113	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	Q₈×C₆₇	—	8	2	no	—
115	Q₈×C₆₇	—	8	2	no	—
116	C₂×C₄×C₆₇	—	2	1	no	—
117	C₂×C₄×C₆₇	—	2	1	no	—
118	C₂×C₄×C₆₇	—	2	1	no	—
119	C₂×C₄×C₆₇	—	2	1	no	—
120	C₂×C₄×C₆₇	—	2	1	no	—
121	C₂×C₄×C₆₇	—	2	1	no	—
122	C₂×C₄×C₆₇	—	2	2	no	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	4	no	—
125	C₂×C₄×C₆₇	—	2	4	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	1	no	—
129	C₂×C₄×C₆₇	—	2	1	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	4	4	no	—
132	C₂×C₄×C₆₇	—	4	2	no	—
133	C₂×C₄×C₆₇	—	4	2	no	—
134	C₂×C₄×C₆₇	—	4	2	no	—
135	C₂×C₄×C₆₇	—	4	2	no	—
136	C₂×C₄×C₆₇	—	4	2	no	—
137	C₂×C₄×C₆₇	—	4	2	no	—
138	C₂×C₄×C₆₇	#102	1	2	yes	—
139	C₂×C₄×C₆₇	#103	1	2	yes	—
140	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
142	C₂×C₄×C₆₇	#121	1	2	yes	—
143	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#135	1	2	yes	—
149	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#137	1	1	yes	characteristic
151	C₆₇⋊C₈	—	4	4	no	—
152	C₆₇⋊C₈	—	8	2	no	—
153	C₂²×C₆₇	—	2	2	no	—
154	C₂²×C₆₇	—	2	2	no	—
155	C₂²×C₆₇	—	2	2	no	—
156	C₂²×C₆₇	—	2	2	no	—
157	C₂²×C₆₇	—	2	2	no	—
158	C₂²×C₆₇	—	2	2	no	—
159	C₂²×C₆₇	#332	1	4	yes	complemented
160	C₂²×C₆₇	#386	1	1	yes	characteristic
161	C₂²×C₆₇	C₂×#101	1	1	yes	characteristic
162	C₂²×C₆₇	#413	1	1	yes	characteristic
163	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
164	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
165	C₂²×C₆₇	#416	1	1	yes	characteristic
166	C₂²×C₆₇	#417	1	1	yes	characteristic
167	C₄×C₆₇	—	2	2	no	—
168	C₄×C₆₇	—	2	2	no	—
169	C₄×C₆₇	—	2	2	no	—
170	C₄×C₆₇	—	4	1	no	—
171	C₄×C₆₇	—	8	2	no	—
172	C₄×C₆₇	—	8	2	no	—
173	C₄×C₆₇	#450	1	1	yes	characteristic
174	C₄×C₆₇	#451	1	1	yes	characteristic
175	C₄×C₆₇	#465	1	2	yes	—
176	C₄×C₆₇	#466	1	2	yes	—
177	C₄×C₆₇	#483	1	1	yes	characteristic
178	C₄×C₆₇	#484	1	1	yes	characteristic
179	#9129	—	67	1	no	maximal, Sylow
180	C₂×C₆₇	—	2	4	no	—
181	C₂×C₆₇	C₂×#332	1	1	yes	characteristic
182	C₂×C₆₇	#1542	1	1	yes	characteristic
183	C₂×C₆₇	#1547	1	1	yes	characteristic
184	C₂×C₆₇	#1552	1	1	yes	characteristic
185	C₂×C₆₇	#1872	1	1	yes	characteristic
186	C₂×C₆₇	#1893	1	1	yes	characteristic
187	C₂×C₆₇	#1901	1	1	yes	characteristic
188	C₂²×C₄⋊C₈	—	67	1	no	—
189	#2857	D₆₇	1	1	yes	characteristic
190	#1797	—	67	1	no	—
191	C₂×#332	—	67	2	no	—
192	#1296	—	67	2	no	—
193	C₆₇	#9129	1	1	yes	characteristic, complemented, Sylow
194	C₂³×C₈	—	134	1	no	—
195	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
196	C₂×C₂²⋊Q₈	—	2	1	no	—
197	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
198	C₂×C₄⋊C₈	—	67	2	no	—
199	C₂×C₄⋊C₈	—	67	2	no	—
200	C₂×C₄⋊C₈	—	134	4	no	—
201	C₂×C₄⋊C₈	—	134	1	no	—
202	C₂×C₂²⋊C₈	—	134	1	no	—
203	#391	—	2	1	no	—
204	#389	—	2	1	no	—
205	#389	Dic₆₇	1	2	yes	—
206	#384	C₂×D₆₇	1	1	yes	characteristic
207	#380	—	2	1	no	—
208	#380	Dic₆₇	1	2	yes	—
209	#336	—	134	1	no	—
210	#332	—	134	4	no	—
211	C₂²×Q₈	—	2	1	no	—
212	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
213	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
215	C₂²×C₈	—	268	2	no	—
216	C₂²×C₈	—	268	2	no	—
217	C₂²×C₈	—	134	2	no	—
218	C₂²×C₈	—	134	4	no	—
219	C₂²×C₈	—	134	2	no	—
220	C₄⋊Q₈	—	2	2	no	—
221	C₄⋊Q₈	—	2	2	no	—
222	C₂²⋊Q₈	—	4	2	no	—
223	C₂²⋊Q₈	—	4	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
235	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
237	C₄⋊C₈	—	67	4	no	—
238	C₄⋊C₈	—	134	4	no	—
239	C₄⋊C₈	—	134	2	no	—
240	C₄⋊C₈	—	134	2	no	—
241	C₄⋊C₈	—	134	2	no	—
242	C₂²⋊C₈	—	268	2	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	C₂⁴	C₂²⋊Dic₆₇	1	1	yes	characteristic
246	C₂×Q₈	—	4	2	no	—
247	C₂×Q₈	—	4	1	no	—
248	C₂×Q₈	—	4	1	no	—
249	C₂×Q₈	—	4	2	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
264	C₂²×C₄	#11761613	1	2	yes	—
265	C₂²×C₄	#11761615	1	2	yes	—
266	C₂²×C₄	#11761616	1	2	yes	—
267	C₂²×C₄	#11761618	1	2	yes	—
268	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
271	C₂×C₈	—	268	8	no	—
272	C₂×C₈	—	268	2	no	—
273	C₂×C₈	—	268	2	no	—
274	C₂×C₈	—	268	2	no	—
275	C₂×C₈	—	268	2	no	—
276	C₂×C₈	—	268	2	no	—
277	C₂×C₈	—	134	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	1	no	—
282	C₄⋊C₄	—	4	1	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₂²⋊C₄	—	4	4	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	1	no	—
292	C₄²	D₄×D₆₇	1	2	yes	—
293	C₄²	#11761627	1	2	yes	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	#14523962	1	2	yes	—
299	C₂³	#14523964	1	2	yes	—
300	C₂³	#14523967	1	2	yes	—
301	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
302	Q₈	—	8	2	no	—
303	Q₈	—	8	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	#14523964	1	2	yes	—
327	C₂×C₄	#14523967	1	2	yes	—
328	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
329	C₂×C₄	#14524011	1	1	yes	characteristic
330	C₂×C₄	#14524015	1	2	yes	—
331	C₂×C₄	#14524024	1	1	yes	characteristic
332	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
333	C₂×C₄	C₂×#11761615	1	1	yes	characteristic
334	C₂×C₄	C₂×#11761616	1	1	yes	characteristic
335	C₂×C₄	C₂×#11761618	1	1	yes	characteristic
336	C₂×C₄	#14524063	1	2	yes	—
337	C₂×C₄	#14524068	1	1	yes	characteristic
338	C₂×C₄	#14524073	1	1	yes	characteristic
339	C₈	—	268	4	no	—
340	C₈	—	536	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	#16863142	1	4	yes	complemented
348	C₂²	#16863276	1	1	yes	characteristic
349	C₂²	C₂×#14523962	1	1	yes	characteristic
350	C₂²	#16863380	1	1	yes	characteristic
351	C₂²	C₂×#14523964	1	1	yes	characteristic
352	C₂²	C₂×#14523967	1	1	yes	characteristic
353	C₂²	#16863392	1	1	yes	characteristic
354	C₂²	#16863397	1	1	yes	characteristic
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	1	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	#16863546	1	1	yes	characteristic
362	C₄	#16863551	1	1	yes	characteristic
363	C₄	#16863623	1	2	yes	—
364	C₄	#16863630	1	2	yes	—
365	C₄	#16863724	1	1	yes	characteristic
366	C₄	#16863729	1	1	yes	characteristic
367	C₂	—	2	4	no	—
368	C₂	C₂×#16863142	1	1	yes	characteristic
369	C₂	#22558866	1	1	yes	characteristic
370	C₂	#22558886	1	1	yes	characteristic
371	C₂	#22558909	1	1	yes	characteristic
372	C₂	#22560517	1	1	yes	characteristic
373	C₂	#22560638	1	1	yes	characteristic
374	C₂	#22560678	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₆₇
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#2857	C₂
socle	C₂³×C₆₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₆₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#2857	D₆₇
hypocenter	C₆₇	#9129
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2857

Complements

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

N	H ≅ G/N	type
3. C₂×#16863142	C₂	semidirect
4. #22558092	C₂	semidirect
159. C₂²×C₆₇	#332	semidirect
193. C₆₇	#9129	semidirect
347. C₂²	#16863142	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₆₇⋊C₈)	2
#22560189	2
C₂×#16863142	2
#22558092	2
C₆₇×#2857	2
#9129	67