Subgroups — #36378732

Order 22592.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₂×#13083443)⋊C₄	C₂	1	6	yes	maximal
2	C₄²×D₃₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13083443	C₂²	1	4	yes	—
4	C₂×C₄×D₃₅₃	C₂²	1	3	yes	—
5	C₄×Dic₃₅₃	C₄	1	3	yes	complemented
6	C₄²×C₃₅₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#13083443	—	2	12	no	—
8	C₂²×D₃₅₃	C₂³	1	1	yes	characteristic
9	C₂×Dic₃₅₃	C₂×C₄	1	3	yes	—
10	C₄×D₃₅₃	—	2	6	no	—
11	C₂×C₄×C₃₅₃	C₂×C₄	1	3	yes	—
12	C₂²×C₃₅₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×D₃₅₃	#41	1	6	yes	—
14	#13083443	—	4	4	no	—
15	C₄×C₃₅₃	—	2	3	no	—
16	Dic₃₅₃	—	2	3	no	—
17	C₂×C₃₅₃	#117	1	3	yes	—
18	D₃₅₃	#126	1	4	yes	—
19	C₃₅₃	#383	1	1	yes	characteristic, complemented, Sylow
20	#383	—	353	1	no	maximal, Sylow
21	C₂×C₄²	—	353	1	no	—
22	#95	—	353	6	no	—
23	C₂²×C₄	—	353	3	no	—
24	C₂²×C₄	—	353	4	no	—
25	C₄²	—	353	3	no	—
26	C₄²	#13083443	1	1	yes	characteristic, complemented
27	C₂³	—	353	1	no	—
28	C₂×C₄	—	353	3	no	—
29	C₂×C₄	—	706	6	no	—
30	C₂×C₄	—	706	12	no	—
31	C₂×C₄	C₂×#13083443	1	3	yes	—
32	C₂²	—	353	6	no	—
33	C₂²	C₂²×#13083443	1	1	yes	characteristic
34	C₄	—	2	3	no	—
35	C₄	—	1412	4	no	—
36	C₄	—	706	3	no	—
37	C₂	—	353	4	no	—
38	C₂	#26015071	1	3	yes	—

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

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