Finite Group DatabasebetaFinite Group DatabasebetaOrder 8991.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #15688500 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C27×C37 | C9 | 1 | 1 | yes | characteristic |
| 3 | C9×C37 | C27 | 1 | 1 | yes | characteristic |
| 4 | C243 | — | 37 | 1 | no | maximal, Sylow |
| 5 | C3×C37 | C81 | 1 | 1 | yes | characteristic |
| 6 | C81 | — | 37 | 1 | no | — |
| 7 | C37 | C243 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C27 | #66526 | 1 | 1 | yes | characteristic |
| 9 | C9 | #11758603 | 1 | 1 | yes | characteristic |
| 10 | C3 | #15688534 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C27 | #66526 |
| commutator, hypocenter | C37 | C243 |
| Fitting | C27×C37 | C9 |
| socle | C3×C37 | C81 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C27 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C37 | C243 | semidirect |