Finite Group DatabasebetaFinite Group DatabasebetaOrder 32157.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #24924310 | C3 | 1 | 3 | yes | maximal, complemented |
| 2 | C9×C397⋊C3 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×C397⋊C3 | C9 | 1 | 1 | yes | characteristic |
| 4 | C9×C397 | C9 | 1 | 1 | yes | characteristic |
| 5 | #16813208 | C9 | 1 | 1 | yes | characteristic |
| 6 | #16813208 | C32 | 1 | 1 | yes | characteristic |
| 7 | C3×C397 | C3×C9 | 1 | 1 | yes | characteristic |
| 8 | C397⋊C3 | C27 | 1 | 3 | yes | complemented |
| 9 | C397 | C3×C27 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C3×C27 | — | 397 | 1 | no | maximal, Sylow |
| 11 | C3×C9 | — | 397 | 1 | no | — |
| 12 | C27 | — | 397 | 3 | no | — |
| 13 | C32 | — | 397 | 1 | no | — |
| 14 | C9 | — | 397 | 1 | no | — |
| 15 | C9 | — | 397 | 1 | no | — |
| 16 | C9 | #16813210 | 1 | 1 | yes | characteristic |
| 17 | C3 | — | 397 | 3 | no | — |
| 18 | C3 | C3×#16813210 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #16813210 |
| commutator, hypocenter | C397 | C3×C27 |
| Frattini | C3 | C3×#16813210 |
| Fitting | C9×C397 | C9 |
| socle | C3×C397 | C3×C9 |
| prime radical | C3×C397⋊C3 | C9 |
| cosocle | #16813208 | C32 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24924310 | C3 | semidirect |
| 8. C397⋊C3 | C27 | semidirect |
| 9. C397 | C3×C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924310 | 3 |
| C9×C397⋊C3 | 3 |
| C3×C27 | 397 |