Finite Group DatabasebetaFinite Group DatabasebetaOrder 10548.
20 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3⋊D879 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C32×C293 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | D879 | — | 6 | 2 | no | — |
| 4 | #11924078 | — | 9 | 1 | no | maximal, Hall |
| 5 | C3×C293 | — | 2 | 2 | no | — |
| 6 | D293 | — | 9 | 1 | no | — |
| 7 | C293 | #157 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | #157 | — | 293 | 1 | no | maximal, Hall |
| 9 | C3⋊D3 | — | 293 | 1 | no | — |
| 10 | C32 | #11924078 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | D3 | — | 1758 | 2 | no | — |
| 12 | C4 | — | 2637 | 1 | no | Sylow |
| 13 | C3 | — | 2 | 2 | no | — |
| 14 | C2 | — | 2637 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C293 | C4 |
| prime radical, cosocle | C3⋊D879 | C2 |
| LCS | G ▷ C32×C293 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×C293 | C4 | semidirect |
| 7. C293 | #157 | semidirect |
| 10. C32 | #11924078 | semidirect |