Subgroups — #10813655

Order 768.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#79012	C₂	1	2	yes	maximal, complemented
2	C₂×#4700	C₂	1	2	yes	maximal
3	C₄×#904	C₂	1	1	yes	maximal, characteristic
4	C₃×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#69794	C₂	1	2	yes	maximal, complemented
6	#69792	C₂	1	1	yes	maximal, characteristic, complemented
7	#69494	C₂	1	2	yes	maximal, complemented
8	#68694	C₂	1	4	yes	maximal, complemented
9	#22688	—	3	1	no	maximal, Sylow
10	C₂×#904	C₂²	1	1	yes	characteristic
11	C₂×#901	C₂²	1	4	yes	—
12	C₄×#235	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×C₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	#5113	C₂²	1	2	yes	—
18	C₂×#819	C₂²	1	2	yes	—
19	C₂×#819	C₂²	1	2	yes	—
20	#5106	C₂²	1	1	yes	characteristic
21	#5102	C₂²	1	4	yes	—
22	C₂×#805	C₂²	1	4	yes	—
23	#4924	C₂²	1	2	yes	—
24	#4839	—	2	4	no	—
25	#4837	—	2	2	no	—
26	D₃×C₄⋊C₈	—	2	2	no	—
27	#4700	—	2	8	no	—
28	C₄×Dic₁₂	C₄	1	1	yes	characteristic, complemented
29	C₄×Dic₁₂	C₄	1	1	yes	characteristic, complemented
30	C₄×D₂₄	C₄	1	1	yes	characteristic, complemented
31	C₄×D₂₄	C₄	1	1	yes	characteristic, complemented
32	C₄×#204	C₄	1	2	yes	complemented
33	C₄×#204	C₄	1	2	yes	complemented
34	C₃×#336	C₂²	1	2	yes	—
35	#4523	C₂²	1	4	yes	—
36	C₂×#443	—	3	2	no	—
37	C₄×#135	—	3	1	no	—
38	#2906	—	3	2	no	—
39	#1945	—	3	2	no	—
40	#1866	—	3	4	no	—
41	#1848	—	3	1	no	—
42	#1806	—	3	2	no	—
43	C₈×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
44	C₂×#235	C₂³	1	2	yes	—
45	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₈	C₂³	1	2	yes	—
47	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₃×C₄²	C₂³	1	2	yes	—
50	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
51	C₄×#67	—	2	2	no	—
52	C₄×#67	—	2	2	no	—
53	#926	C₂³	1	2	yes	—
54	C₂×#208	C₂³	1	4	yes	—
55	C₂×Dic₁₂	C₂×C₄	1	1	yes	characteristic
56	#904	D₄	1	4	yes	—
57	#904	Q₈	1	4	yes	—
58	C₂×D₂₄	C₂×C₄	1	1	yes	characteristic
59	C₂×#204	C₂×C₄	1	2	yes	—
60	#901	—	2	8	no	—
61	#901	—	4	4	no	—
62	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
63	C₂×D₃×C₈	—	2	4	no	—
64	C₄×D₁₂	C₂×C₄	1	2	yes	—
65	C₄×D₁₂	C₂×C₄	1	2	yes	—
66	#872	—	2	2	no	—
67	C₄²×D₃	—	2	2	no	—
68	C₄×Dic₆	C₂×C₄	1	2	yes	—
69	C₄×Dic₆	C₂×C₄	1	2	yes	—
70	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
71	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
72	C₃×C₄⋊C₈	D₄	1	2	yes	—
73	C₃×C₄×C₈	—	2	4	no	—
74	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
75	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
76	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
77	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
78	C₃×#95	—	2	1	no	—
79	#821	C₂×C₄	1	2	yes	—
80	#821	C₂×C₄	1	2	yes	—
81	#819	—	2	4	no	—
82	#819	—	4	2	no	—
83	#818	C₂×C₄	1	1	yes	characteristic
84	#818	C₂×C₄	1	1	yes	characteristic
85	#817	C₂×C₄	1	2	yes	—
86	#816	C₂×C₄	1	2	yes	—
87	#816	C₂×C₄	1	2	yes	—
88	Dic₃⋊C₈	—	2	4	no	—
89	Dic₃⋊C₈	—	2	4	no	—
90	#805	—	2	8	no	—
91	C₄⋊(C₃⋊C₈)	—	2	2	no	—
92	C₄⋊(C₃⋊C₈)	—	2	2	no	—
93	C₂×#135	—	3	1	no	—
94	C₂×#131	—	3	4	no	—
95	C₄×#41	—	3	2	no	—
96	#443	—	6	8	no	—
97	C₄×Q₁₆	—	3	1	no	—
98	C₄×Q₁₆	—	3	1	no	—
99	C₄×SD₁₆	—	3	2	no	—
100	C₄×SD₁₆	—	3	2	no	—
101	C₄×D₈	—	3	1	no	—
102	C₄×D₈	—	3	1	no	—
103	C₂×#108	—	3	2	no	—
104	C₂×#108	—	3	2	no	—
105	#427	—	3	1	no	—
106	#424	—	3	4	no	—
107	#424	—	6	4	no	—
108	#423	—	3	2	no	—
109	#423	—	6	2	no	—
110	C₂×C₄⋊C₈	—	6	2	no	—
111	C₂×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
112	C₂×#104	—	3	4	no	—
113	#416	—	3	2	no	—
114	C₂×C₄×C₈	C₂×D₃	1	2	yes	—
115	C₂×C₄×C₈	C₂×D₃	1	1	yes	characteristic
116	C₄×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
117	#339	—	3	4	no	—
118	#336	C₂×D₃	1	2	yes	—
119	C₂²×C₃×C₄	—	2	2	no	—
120	C₂²×C₃×C₄	#41	1	1	yes	characteristic
121	C₂²×C₃×C₄	#41	1	1	yes	characteristic
122	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
123	C₂×#67	—	2	2	no	—
124	#235	—	2	2	no	—
125	#235	—	2	2	no	—
126	#235	C₂×D₄	1	4	yes	—
127	#235	C₂×Q₈	1	4	yes	—
128	C₂×D₁₂	C₂²×C₄	1	2	yes	—
129	C₂×C₄×D₃	—	2	2	no	—
130	C₂×C₄×D₃	—	2	2	no	—
131	C₂×C₄×D₃	—	2	2	no	—
132	C₂×Dic₆	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₈	—	2	2	no	—
134	C₂×C₃×C₈	—	2	1	no	—
135	C₂×C₃×C₈	—	2	2	no	—
136	C₂×C₃×C₈	—	2	1	no	—
137	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₈	C₂×Q₈	1	2	yes	—
145	C₃×C₄⋊C₄	—	2	4	no	—
146	C₃×C₄²	—	2	2	no	—
147	C₃×C₄²	—	2	2	no	—
148	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
149	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
150	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
151	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
152	#217	—	2	2	no	—
153	(C₂×D₃)⋊C₄	—	2	2	no	—
154	(C₂×D₃)⋊C₄	—	2	2	no	—
155	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
156	C₄⋊Dic₃	C₂²×C₄	1	2	yes	—
157	Dic₃⋊C₄	—	2	2	no	—
158	Dic₃⋊C₄	—	2	2	no	—
159	C₄×Dic₃	—	2	2	no	—
160	C₄×Dic₃	—	2	2	no	—
161	C₄×Dic₃	—	2	2	no	—
162	#208	—	2	4	no	—
163	#208	—	2	4	no	—
164	C₂×C₃⋊C₈	—	2	4	no	—
165	Dic₁₂	C₄⋊C₄	1	4	yes	complemented
166	D₂₄	C₄⋊C₄	1	4	yes	complemented
167	#204	C₄⋊C₄	1	8	yes	complemented
168	ΓL(1,𝔽₂₅)	—	4	8	no	—
169	D₃×C₈	—	4	8	no	—
170	C₂×#41	—	3	2	no	—
171	#135	—	3	4	no	—
172	#135	—	3	4	no	—
173	C₂×Q₁₆	—	3	1	no	—
174	C₂×SD₁₆	—	3	2	no	—
175	C₂×D₈	—	3	1	no	—
176	#131	—	6	8	no	—
177	#131	—	12	4	no	—
178	C₂×M₁₆	—	3	4	no	—
179	C₂×M₁₆	—	6	4	no	—
180	C₂²×C₈	—	6	4	no	—
181	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₈	C₂²×D₃	1	2	yes	—
183	C₂²×C₈	C₂²×D₃	1	1	yes	characteristic
184	C₄×Q₈	—	3	2	no	—
185	C₄×Q₈	—	3	2	no	—
186	C₄×D₄	—	3	2	no	—
187	C₄×D₄	—	3	2	no	—
188	C₄×D₄	—	6	2	no	—
189	C₄×D₄	—	6	2	no	—
190	#117	—	3	2	no	—
191	#117	—	6	2	no	—
192	C₂×C₄⋊C₄	—	2	1	no	—
193	C₂×C₄²	—	6	2	no	—
194	C₂×C₄²	C₂²×D₃	1	2	yes	—
195	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
196	#108	—	6	4	no	—
197	#108	—	12	2	no	—
198	#107	—	3	1	no	—
199	#107	—	3	1	no	—
200	#106	—	3	2	no	—
201	C₄⋊C₈	—	6	4	no	—
202	C₄⋊C₈	—	6	4	no	—
203	C₄⋊C₈	—	6	2	no	—
204	C₄⋊C₈	—	6	2	no	—
205	C₄⋊C₈	D₁₂	1	1	yes	characteristic
206	C₄⋊C₈	D₁₂	1	1	yes	characteristic
207	C₄⋊C₈	D₁₂	1	2	yes	—
208	#104	—	6	8	no	—
209	#103	—	3	2	no	—
210	#103	—	3	2	no	—
211	#102	—	3	2	no	—
212	#102	—	3	2	no	—
213	C₄×C₈	—	2	4	no	—
214	C₄×C₈	C₄×D₃	1	1	yes	characteristic
215	C₄×C₈	C₄×D₃	1	1	yes	characteristic
216	C₄×C₈	C₄×D₃	1	1	yes	characteristic
217	C₄×C₈	C₄×D₃	1	1	yes	characteristic
218	#95	—	2	1	no	—
219	C₂³×C₃	C₂×#41	1	1	yes	characteristic
220	C₂²×D₃	—	2	2	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	4	1	no	—
224	C₂×C₃×C₄	—	4	2	no	—
225	C₂×C₃×C₄	—	4	2	no	—
226	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
234	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₃×C₄	2₋¹⁺⁴	1	1	yes	characteristic
236	#67	—	2	4	no	—
237	#67	—	2	4	no	—
238	C₂×Dic₃	—	2	2	no	—
239	C₂×Dic₃	—	2	2	no	—
240	C₂×Dic₃	—	2	2	no	—
241	D₁₂	—	2	2	no	—
242	D₁₂	C₂×C₄⋊C₄	1	4	yes	—
243	C₄×D₃	—	2	4	no	—
244	C₄×D₃	—	2	4	no	—
245	C₄×D₃	—	4	4	no	—
246	C₄×D₃	—	8	2	no	—
247	Dic₆	—	2	2	no	—
248	Dic₆	C₂×C₄⋊C₄	1	4	yes	—
249	C₃×C₈	—	2	1	no	—
250	C₃×C₈	—	2	1	no	—
251	C₃×C₈	—	2	2	no	—
252	C₃×C₈	—	2	2	no	—
253	C₃×C₈	C₂×C₄⋊C₄	1	2	yes	—
254	C₃×C₈	C₂×C₄⋊C₄	1	2	yes	—
255	C₃⋊C₈	—	4	4	no	—
256	#41	—	3	4	no	—
257	#41	—	3	4	no	—
258	#41	—	6	2	no	—
259	#41	—	6	2	no	—
260	C₂×Q₈	—	3	2	no	—
261	C₂×D₄	—	3	2	no	—
262	C₂×D₄	—	6	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	6	2	no	—
265	C₂²×C₄	—	6	2	no	—
266	C₂²×C₄	—	6	2	no	—
267	C₂²×C₄	#235	1	1	yes	characteristic
268	C₂²×C₄	#235	1	1	yes	characteristic
269	C₂²×C₄	C₂³×D₃	1	1	yes	characteristic
270	Q₁₆	—	3	4	no	—
271	SD₁₆	—	3	8	no	—
272	D₈	—	3	4	no	—
273	M₁₆	—	6	4	no	—
274	M₁₆	—	6	4	no	—
275	M₁₆	—	12	8	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	6	4	no	—
281	C₂×C₈	—	12	8	no	—
282	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
283	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₈	C₂×C₄×D₃	1	1	yes	characteristic
286	C₂×C₈	C₂×D₁₂	1	2	yes	—
287	C₂×C₈	C₂×D₁₂	1	2	yes	—
288	C₂×C₈	D₃×D₄	1	2	yes	—
289	C₂×C₈	D₃×Q₈	1	2	yes	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	3	2	no	—
292	C₄⋊C₄	—	3	2	no	—
293	C₄⋊C₄	—	6	2	no	—
294	C₄⋊C₄	—	6	2	no	—
295	C₂²⋊C₄	—	6	2	no	—
296	C₂²⋊C₄	—	6	2	no	—
297	C₂²⋊C₄	—	6	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	6	2	no	—
301	C₄²	—	6	2	no	—
302	C₄²	—	6	2	no	—
303	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
304	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
305	C₄²	C₂×D₁₂	1	1	yes	characteristic
306	C₄²	C₂×D₁₂	1	1	yes	characteristic
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₃	#547	1	1	yes	characteristic
311	C₂²×C₃	#554	1	1	yes	characteristic
312	C₂×D₃	—	2	4	no	—
313	C₂×D₃	—	4	2	no	—
314	C₂×D₃	—	4	2	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	4	4	no	—
319	C₃×C₄	#443	1	2	yes	complemented
320	C₃×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
321	C₃×C₄	#520	1	1	yes	characteristic
322	C₃×C₄	D₄²	1	1	yes	characteristic
323	C₃×C₄	D₄×Q₈	1	1	yes	characteristic
324	Dic₃	—	2	4	no	—
325	Dic₃	—	4	2	no	—
326	Dic₃	—	4	2	no	—
327	C₂³	—	6	2	no	—
328	C₂³	C₂×#235	1	1	yes	characteristic
329	Q₈	—	3	4	no	—
330	Q₈	—	6	2	no	—
331	D₄	—	3	4	no	—
332	D₄	—	6	4	no	—
333	D₄	—	6	4	no	—
334	D₄	—	6	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	6	2	no	—
341	C₂×C₄	—	6	4	no	—
342	C₂×C₄	—	6	4	no	—
343	C₂×C₄	—	6	2	no	—
344	C₂×C₄	—	6	2	no	—
345	C₂×C₄	—	12	4	no	—
346	C₂×C₄	—	24	2	no	—
347	C₂×C₄	C₄×D₁₂	1	1	yes	characteristic
348	C₂×C₄	C₄×D₁₂	1	1	yes	characteristic
349	C₂×C₄	C₄×D₁₂	1	1	yes	characteristic
350	C₂×C₄	C₄×D₁₂	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₁₂	1	1	yes	characteristic
353	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
355	C₂×C₄	#1009	1	1	yes	characteristic
356	C₂×C₄	#1010	1	1	yes	characteristic
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	12	4	no	—
362	C₈	D₃×C₄⋊C₄	1	2	yes	—
363	C₈	D₃×C₄⋊C₄	1	2	yes	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	D₄×C₄⋊C₄	1	1	yes	characteristic
367	C₂×C₃	C₂×#443	1	1	yes	characteristic
368	C₂×C₃	#2957	1	1	yes	characteristic
369	D₃	—	4	4	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	6	4	no	—
373	C₂²	—	12	2	no	—
374	C₂²	—	12	2	no	—
375	C₂²	C₂×C₄×D₁₂	1	1	yes	characteristic
376	C₂²	#5551	1	1	yes	characteristic
377	C₂²	#5579	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	4	no	—
382	C₄	—	6	4	no	—
383	C₄	—	12	2	no	—
384	C₄	—	12	2	no	—
385	C₄	#4700	1	2	yes	complemented
386	C₄	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
387	C₄	#5523	1	1	yes	characteristic
388	C₄	D₄×D₁₂	1	1	yes	characteristic
389	C₄	Q₈×D₁₂	1	1	yes	characteristic
390	C₃	#22688	1	1	yes	characteristic, complemented, Sylow
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	12	4	no	—
394	C₂	C₄⋊C₄×D₁₂	1	1	yes	characteristic
395	C₂	C₂×#4700	1	1	yes	characteristic
396	C₂	#78580	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₂
commutator	C₂×C₃×C₄	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₃
Fitting	C₃×C₈×C₄⋊C₄	C₂
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₂×#904	C₂²
cosocle	C₂²×C₃×C₄	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₃
hypocenter	C₃	#22688
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #79012	C₂	semidirect
4. C₃×C₈×C₄⋊C₄	C₂	semidirect
5. #69794	C₂	semidirect
6. #69792	C₂	semidirect
7. #69494	C₂	semidirect
8. #68694	C₂	semidirect
28. C₄×Dic₁₂	C₄	semidirect
29. C₄×Dic₁₂	C₄	semidirect
30. C₄×D₂₄	C₄	semidirect
31. C₄×D₂₄	C₄	semidirect
32. C₄×#204	C₄	semidirect
33. C₄×#204	C₄	semidirect
43. C₈×C₄⋊C₄	D₃	semidirect
165. Dic₁₂	C₄⋊C₄	semidirect
166. D₂₄	C₄⋊C₄	semidirect
167. #204	C₄⋊C₄	semidirect
319. C₃×C₄	#443	semidirect
385. C₄	#4700	semidirect
390. C₃	#22688	semidirect

Maximal subgroups

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

subgroup	index
#79012	2
C₂×#4700	2
C₄×#904	2
C₃×C₈×C₄⋊C₄	2
#69794	2
#69792	2
#69494	2
#68694	2
#22688	3