Finite Group DatabasebetaFinite Group DatabasebetaOrder 6054.
8 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C1009⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D1009 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C1009 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 4 | C2×C3 | — | 1009 | 1 | no | maximal, Hall |
| 5 | C3 | — | 1009 | 1 | no | Sylow |
| 6 | C2 | — | 1009 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1009 | C2×C3 |
| LCS | G ▷ C1009 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C1009⋊C3 | C2 | semidirect |
| 2. D1009 | C3 | semidirect |
| 3. C1009 | C2×C3 | semidirect |