Subgroups — C₂₃×#10624500 #30661007

Order 16767.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₈₁⋊C₃	C₃	1	3	yes	maximal
2	C₂₃×#6864	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₃×C₂₇	C₉	1	2	yes	—
4	C₃×C₂₃×C₂₇	C₃²	1	1	yes	characteristic
5	C₉²×C₂₃	C₉	1	1	yes	characteristic
6	C₂₃×C₈₁	C₉	1	9	yes	complemented
7	#10624500	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃×C₉×C₂₃	—	3	1	no	—
9	C₃×C₉×C₂₃	C₃×C₉	1	1	yes	characteristic
10	C₂₃×C₂₇	—	3	2	no	—
11	C₂₃×C₂₇	C₃×C₉	1	3	yes	—
12	C₈₁⋊C₃	C₃×C₂₃	1	3	yes	—
13	#6864	C₃×C₂₃	1	1	yes	characteristic
14	C₃²×C₂₃	C₂₇⋊C₃	1	1	yes	characteristic
15	C₉×C₂₃	—	9	1	no	—
16	C₉×C₂₃	C₉²	1	1	yes	characteristic
17	C₉×C₂₃	C₂₇⋊C₃	1	2	yes	—
18	C₃×C₂₇	C₉×C₂₃	1	2	yes	—
19	C₃×C₂₇	C₃²×C₂₃	1	1	yes	characteristic
20	C₉²	C₉×C₂₃	1	1	yes	characteristic
21	C₈₁	C₉×C₂₃	1	9	yes	complemented
22	C₃×C₂₃	—	3	1	no	—
23	C₃×C₂₃	#6864	1	1	yes	characteristic
24	C₃×C₉	—	3	1	no	—
25	C₃×C₉	C₃×C₉×C₂₃	1	1	yes	characteristic
26	C₂₇	—	3	2	no	—
27	C₂₇	C₃×C₉×C₂₃	1	3	yes	—
28	C₂₃	#10624500	1	1	yes	characteristic, direct product factor, Sylow
29	C₃²	C₂₃×C₂₇⋊C₃	1	1	yes	characteristic
30	C₉	—	9	1	no	—
31	C₉	C₉²×C₂₃	1	1	yes	characteristic
32	C₉	C₂₃×C₂₇⋊C₃	1	2	yes	—
33	C₃	—	3	1	no	—
34	C₃	C₂₃×#6864	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.