Finite Group DatabasebetaFinite Group DatabasebetaOrder 7533.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #14578902 | C3 | 1 | 2 | yes | maximal, complemented |
| 2 | #14578900 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C31×C9⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×C9×C31 | — | 3 | 1 | no | — |
| 5 | C3×C9×C31 | C32 | 1 | 1 | yes | characteristic |
| 6 | C32⋊(C31⋊C3) | — | 3 | 1 | no | — |
| 7 | #11719689 | — | 3 | 2 | no | — |
| 8 | C32×C31 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 9 | C3×C31⋊C3 | — | 9 | 1 | no | — |
| 10 | C9×C31 | — | 3 | 1 | no | — |
| 11 | C9×C31 | — | 9 | 1 | no | — |
| 12 | C31⋊C9 | — | 9 | 2 | no | — |
| 13 | #6883 | — | 31 | 1 | no | maximal, Sylow |
| 14 | C3×C31 | — | 3 | 1 | no | — |
| 15 | C3×C31 | #732 | 1 | 1 | yes | characteristic |
| 16 | C31⋊C3 | — | 27 | 1 | no | — |
| 17 | #733 | — | 31 | 2 | no | — |
| 18 | #732 | — | 31 | 1 | no | — |
| 19 | C9⋊C9 | C31⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C31 | #6883 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | 3−1+2 | — | 93 | 2 | no | — |
| 22 | H(3,𝔽3) | — | 93 | 1 | no | — |
| 23 | C3×C9 | — | 3 | 1 | no | — |
| 24 | C3×C9 | C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 25 | C32 | — | 279 | 1 | no | — |
| 26 | C32 | C32⋊(C31⋊C3) | 1 | 1 | yes | characteristic |
| 27 | C9 | — | 3 | 1 | no | — |
| 28 | C9 | — | 9 | 1 | no | — |
| 29 | C9 | — | 279 | 2 | no | — |
| 30 | C3 | — | 3 | 1 | no | — |
| 31 | C3 | — | 837 | 1 | no | — |
| 32 | C3 | #14578900 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14578902 | C3 | semidirect |
| 3. C31×C9⋊C9 | C3 | semidirect |
| 19. C9⋊C9 | C31⋊C3 | semidirect |
| 20. C31 | #6883 | semidirect |