Finite Group DatabasebetaFinite Group DatabasebetaOrder 7533.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #14578892 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14578892 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14578886 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | C31×C27⋊C3 | C3 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×C9×C31 | C32 | 1 | 1 | yes | characteristic |
| 6 | C3×C31⋊C9 | — | 3 | 1 | no | — |
| 7 | C27×C31 | — | 3 | 1 | no | — |
| 8 | C31⋊C27 | — | 3 | 1 | no | — |
| 9 | C31⋊C27 | C9 | 1 | 3 | yes | complemented |
| 10 | C32×C31 | 3−1+2 | 1 | 1 | yes | characteristic |
| 11 | C9×C31 | C3×C9 | 1 | 1 | yes | characteristic |
| 12 | C9×C31 | 3−1+2 | 1 | 1 | yes | characteristic |
| 13 | C9×C31 | 3−1+2 | 1 | 1 | yes | characteristic |
| 14 | C31⋊C9 | — | 9 | 1 | no | — |
| 15 | #6875 | — | 31 | 1 | no | maximal, Sylow |
| 16 | C3×C31 | — | 3 | 1 | no | — |
| 17 | C3×C31 | C9⋊C9 | 1 | 1 | yes | characteristic |
| 18 | C27⋊C3 | — | 31 | 1 | no | — |
| 19 | C27⋊C3 | — | 31 | 1 | no | — |
| 20 | C27⋊C3 | C31⋊C3 | 1 | 1 | yes | characteristic |
| 21 | C9⋊C9 | — | 31 | 1 | no | — |
| 22 | C31 | #6875 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 23 | C3×C9 | — | 93 | 1 | no | — |
| 24 | C3×C9 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 25 | C27 | — | 3 | 1 | no | — |
| 26 | C27 | — | 31 | 3 | no | — |
| 27 | C27 | — | 93 | 1 | no | — |
| 28 | C32 | #11719686 | 1 | 1 | yes | characteristic |
| 29 | C9 | — | 279 | 1 | no | — |
| 30 | C9 | C9×C31⋊C3 | 1 | 1 | yes | characteristic |
| 31 | C9 | #11719687 | 1 | 1 | yes | characteristic |
| 32 | C9 | #11719689 | 1 | 1 | yes | characteristic |
| 33 | C3 | — | 3 | 1 | no | — |
| 34 | C3 | (C31⋊C9)⋊C9 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C31⋊C27 | C9 | semidirect |
| 22. C31 | #6875 | semidirect |