Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
4414 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C36 | C13 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C33⋊C13 | — | 27 | 28 | no | maximal |
| 3 | C35 | — | 13 | 28 | no | — |
| 4 | C34 | — | 13 | 819 | no | — |
| 5 | C34 | — | 13 | 28 | no | — |
| 6 | C33 | — | 13 | 1092 | no | — |
| 7 | C33 | — | 13 | 1512 | no | — |
| 8 | C33 | C33⋊C13 | 1 | 28 | yes | complemented |
| 9 | C13 | — | 729 | 1 | no | Sylow |
| 10 | C32 | — | 13 | 28 | no | — |
| 11 | C32 | — | 13 | 819 | no | — |
| 12 | C3 | — | 13 | 28 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C36 | C13 |
| LCS | G ▷ C36 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C36 | C13 | semidirect |
| 8. C33 | C33⋊C13 | semidirect |