Subgroups — C₄⋊#15667734 #26015085

Order 11296.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15667734	C₂	1	2	yes	maximal
2	C₄×#13083443	C₂	1	1	yes	maximal, characteristic
3	#15667734	—	2	2	no	—
4	C₂×#13083443	C₄	1	1	yes	characteristic
5	C₂×#13083443	C₂²	1	1	yes	characteristic
6	C₄×D₃₅₃	C₄	1	1	yes	characteristic
7	C₂×D₃₅₃	C₂×C₄	1	1	yes	characteristic
8	#13083443	—	2	1	no	—
9	#13083443	D₄	1	1	yes	characteristic
10	#13083443	Q₈	1	1	yes	characteristic
11	C₄×C₃₅₃	C₈	1	1	yes	characteristic, complemented
12	Dic₃₅₃	C₈	1	1	yes	characteristic, complemented
13	C₂×C₃₅₃	C₂×C₈	1	1	yes	characteristic
14	D₃₅₃	C₄⋊C₄	1	1	yes	characteristic
15	D₃₅₃	M₁₆	1	1	yes	characteristic
16	C₃₅₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
17	C₄⋊C₈	—	353	1	no	maximal, Sylow
18	C₂×C₈	—	353	2	no	—
19	C₄²	—	353	1	no	—
20	C₂×C₄	—	353	1	no	—
21	C₂×C₄	—	353	1	no	—
22	C₂×C₄	—	353	1	no	—
23	C₈	—	706	2	no	—
24	C₂²	—	353	1	no	—
25	C₄	—	353	1	no	—
26	C₄	—	353	1	no	—
27	C₄	—	353	1	no	—
28	C₄	—	706	1	no	—
29	C₄	#15667734	1	1	yes	characteristic, complemented
30	C₂	—	353	1	no	—
31	C₂	—	353	1	no	—
32	C₂	C₂×#15667734	1	1	yes	characteristic

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.