Finite Group DatabasebetaFinite Group DatabasebetaOrder 24867.
28 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22552079 | C3 | 1 | 3 | yes | maximal, direct product factor |
| 2 | C3×#14583772 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C32×C307 | C9 | 1 | 1 | yes | characteristic |
| 4 | #14583772 | C9 | 1 | 2 | yes | — |
| 5 | #14583772 | C32 | 1 | 1 | yes | characteristic |
| 6 | C3×C307 | C27 | 1 | 3 | yes | complemented |
| 7 | C3×C307 | C3×C9 | 1 | 1 | yes | characteristic |
| 8 | C307 | C3×C27 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C3×C27 | — | 307 | 1 | no | maximal, Sylow |
| 10 | C3×C9 | — | 307 | 1 | no | — |
| 11 | C27 | — | 307 | 3 | no | — |
| 12 | C32 | #14583774 | 1 | 1 | yes | characteristic |
| 13 | C9 | — | 307 | 1 | no | — |
| 14 | C9 | — | 307 | 2 | no | — |
| 15 | C3 | #22552079 | 1 | 3 | yes | direct product factor |
| 16 | C3 | C3×#14583774 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #14583774 |
| commutator, hypocenter | C307 | C3×C27 |
| Frattini | C3 | C3×#14583774 |
| Fitting, socle, prime radical | C32×C307 | C9 |
| cosocle | #14583772 | C32 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22552079 | C3 | direct (N × H) |
| 6. C3×C307 | C27 | semidirect |
| 8. C307 | C3×C27 | semidirect |
| 15. C3 | #22552079 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22552079 | 3 |
| C3×#14583772 | 3 |
| C3×C27 | 307 |