Finite Group DatabasebetaFinite Group DatabasebetaOrder 12178.
4 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C6089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C2 | — | 6089 | 1 | no | maximal, Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6089 | C2 |
| LCS | G ▷ C6089 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C6089 | C2 | semidirect |