Subgroups — (C₂₇⋊C₃)⋊Q₈ #10619604

Order 648.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	(C₂₇⋊C₃)⋊C₄	C₂	1	2	yes	maximal
3	C₃×Dic₁₈	—	3	1	no	maximal
4	Dic₅₄	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₇⋊C₃	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₉	D₃	1	1	yes	characteristic
7	C₃×Dic₉	—	3	2	no	—
8	C₄×C₂₇	—	2	1	no	—
9	C₄×C₂₇	C₂×C₃	1	1	yes	characteristic
10	Dic₂₇	C₂×C₃	1	2	yes	—
11	C₂₇⋊C₃	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₆	—	9	1	no	—
13	Dic₁₈	—	3	1	no	—
14	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
15	C₂×C₂₇	—	2	1	no	—
16	C₂×C₂₇	C₂²×C₃	1	1	yes	characteristic
17	C₃²×C₄	D₉	1	1	yes	characteristic
18	C₃×Dic₃	—	9	2	no	—
19	C₄×C₉	—	2	1	no	—
20	C₄×C₉	C₃×D₃	1	1	yes	characteristic
21	Dic₉	—	3	2	no	—
22	C₃×C₉	Dic₆	1	1	yes	characteristic
23	C₂₇	—	2	1	no	—
24	C₂₇	C₃×Q₈	1	1	yes	characteristic, complemented
25	C₃×Q₈	—	27	1	no	—
26	Dic₆	—	9	1	no	—
27	C₂×C₃²	C₂×D₉	1	1	yes	characteristic
28	C₂×C₉	—	2	1	no	—
29	C₂×C₉	C₂×C₃×D₃	1	1	yes	characteristic
30	C₃×C₄	—	6	1	no	—
31	C₃×C₄	—	27	2	no	—
32	C₃×C₄	C₃×D₉	1	1	yes	characteristic
33	Dic₃	—	9	2	no	—
34	C₃²	Dic₁₈	1	1	yes	characteristic
35	C₉	—	2	1	no	—
36	C₉	C₃×Dic₆	1	1	yes	characteristic
37	Q₈	—	27	1	no	Sylow
38	C₂×C₃	—	6	1	no	—
39	C₂×C₃	C₂×C₃×D₉	1	1	yes	characteristic
40	C₄	—	27	2	no	—
41	C₄	D₂₇⋊C₃	1	1	yes	characteristic
42	C₃	—	6	1	no	—
43	C₃	C₃×Dic₁₈	1	1	yes	characteristic
44	C₂	C₂×D₂₇⋊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.