Subgroups — #67610

Order 384.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₆₄	C₂	1	1	yes	maximal, characteristic
2	Dic₄₈	C₂	1	1	yes	maximal, characteristic
3	C₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
4	Q₁₂₈	—	3	1	no	maximal, Sylow
5	C₃×Q₃₂	—	2	1	no	—
6	Dic₂₄	—	2	1	no	—
7	C₃×C₃₂	C₂²	1	1	yes	characteristic
8	Q₆₄	—	3	1	no	—
9	Q₆₄	D₃	1	1	yes	characteristic
10	C₆₄	—	3	1	no	—
11	C₃×Q₁₆	—	4	1	no	—
12	Dic₁₂	—	4	1	no	—
13	C₃×C₁₆	D₄	1	1	yes	characteristic
14	Q₃₂	—	2	1	no	—
15	Q₃₂	—	6	1	no	—
16	C₃₂	C₂×D₃	1	1	yes	characteristic
17	C₃×Q₈	—	8	1	no	—
18	Dic₆	—	8	1	no	—
19	C₃×C₈	D₈	1	1	yes	characteristic
20	Q₁₆	—	4	1	no	—
21	Q₁₆	—	12	1	no	—
22	C₁₆	#67	1	1	yes	characteristic
23	C₃×C₄	—	16	1	no	—
24	C₃×C₄	D₁₆	1	1	yes	characteristic
25	Dic₃	—	16	1	no	—
26	Q₈	—	8	1	no	—
27	Q₈	—	24	1	no	—
28	C₈	#213	1	1	yes	characteristic
29	C₂×C₃	D₃₂	1	1	yes	characteristic
30	C₄	—	16	1	no	—
31	C₄	—	48	1	no	—
32	C₄	#826	1	1	yes	characteristic
33	C₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
34	C₂	#4519	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₃	Q₁₂₈	semidirect

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