Subgroups — C₃²×#15668887 #40997014

Order 26487.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15668887	C₃	1	12	yes	maximal, direct product factor
2	C₃²×#11758281	C₃	1	1	yes	maximal, characteristic
3	#15668887	C₃²	1	9	yes	direct product factor
4	C₃×#11758281	C₉	1	8	yes	—
5	C₃×#11758281	C₃²	1	4	yes	—
6	C₃²×C₁₀₉⋊C₃	C₉	1	1	yes	characteristic
7	C₃²×C₁₀₉	C₂₇	1	1	yes	characteristic, complemented
8	C₃×C₁₀₉⋊C₃	C₂₇	1	8	yes	complemented
9	C₃×C₁₀₉⋊C₃	C₃×C₉	1	4	yes	—
10	#11758281	C₃×C₉	1	8	yes	—
11	#11758281	C₃³	1	1	yes	characteristic
12	C₃×C₁₀₉	C₃×C₂₇	1	4	yes	complemented
13	C₁₀₉⋊C₃	C₃×C₂₇	1	8	yes	complemented
14	C₁₀₉⋊C₃	C₃²×C₉	1	1	yes	characteristic
15	C₃²×C₂₇	—	109	1	no	maximal, Sylow
16	C₁₀₉	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
17	C₃²×C₉	—	109	1	no	—
18	C₃×C₂₇	—	109	12	no	—
19	C₃³	—	109	1	no	—
20	C₃×C₉	—	109	8	no	—
21	C₃×C₉	—	109	4	no	—
22	C₂₇	—	109	9	no	—
23	C₃²	—	109	4	no	—
24	C₃²	—	109	8	no	—
25	C₃²	#15668887	1	1	yes	characteristic, direct product factor
26	C₉	—	109	1	no	—
27	C₉	—	109	8	no	—
28	C₃	—	109	1	no	—
29	C₃	—	109	8	no	—
30	C₃	C₃×#15668887	1	4	yes	direct product factor

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.