Subgroups — (C₁₃⋊C₃)⋊Q₈ #64592

Order 312.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃⋊C₃	C₂	1	2	yes	maximal
3	Dic₂₆	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
5	C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
6	Dic₁₃	C₂×C₃	1	2	yes	—
7	C₁₃⋊C₃	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₃	C₂²×C₃	1	1	yes	characteristic
9	C₃×Q₈	—	13	1	no	maximal, Hall
10	C₁₃	C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₄	—	13	2	no	—
12	C₃×C₄	—	13	1	no	—
13	Q₈	—	13	1	no	Sylow
14	C₂×C₃	—	13	1	no	—
15	C₄	—	13	2	no	—
16	C₄	D₁₃⋊C₃	1	1	yes	characteristic
17	C₃	—	13	1	no	Sylow
18	C₂	C₂×D₁₃⋊C₃	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.