Subgroups — C₃×C₈×C₂₇ #10619516

Order 648.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₉	C₃	1	1	yes	maximal, characteristic
3	C₈×C₂₇	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃×C₂₇	C₄	1	1	yes	characteristic
5	C₃×C₄×C₉	C₂×C₃	1	1	yes	characteristic
6	C₄×C₂₇	C₂×C₃	1	3	yes	—
7	C₃×C₂₇	C₈	1	1	yes	characteristic, direct product factor, Sylow
8	C₃²×C₈	C₉	1	1	yes	characteristic
9	C₈×C₉	C₉	1	2	yes	—
10	C₈×C₉	C₃²	1	1	yes	characteristic
11	C₂×C₃×C₉	C₃×C₄	1	1	yes	characteristic
12	C₂×C₂₇	C₃×C₄	1	3	yes	—
13	C₃²×C₄	C₂×C₉	1	1	yes	characteristic
14	C₄×C₉	C₂×C₉	1	2	yes	—
15	C₄×C₉	C₂×C₃²	1	1	yes	characteristic
16	C₃×C₉	C₃×C₈	1	1	yes	characteristic
17	C₂₇	C₃×C₈	1	3	yes	direct product factor
18	C₃×C₈	C₂₇	1	3	yes	direct product factor
19	C₃×C₈	C₃×C₉	1	1	yes	characteristic
20	C₂×C₃²	C₄×C₉	1	1	yes	characteristic
21	C₂×C₉	C₄×C₉	1	2	yes	—
22	C₂×C₉	C₃²×C₄	1	1	yes	characteristic
23	C₃×C₄	C₂×C₂₇	1	3	yes	—
24	C₃×C₄	C₂×C₃×C₉	1	1	yes	characteristic
25	C₃²	C₈×C₉	1	1	yes	characteristic
26	C₉	C₈×C₉	1	2	yes	—
27	C₉	C₃²×C₈	1	1	yes	characteristic
28	C₈	C₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃	C₄×C₂₇	1	3	yes	—
30	C₂×C₃	C₃×C₄×C₉	1	1	yes	characteristic
31	C₄	C₂×C₃×C₂₇	1	1	yes	characteristic
32	C₃	C₈×C₂₇	1	3	yes	direct product factor
33	C₃	C₃×C₈×C₉	1	1	yes	characteristic
34	C₂	C₃×C₄×C₂₇	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.