Finite Group DatabasebetaFinite Group DatabasebetaOrder 5427.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C32⋊(C67⋊C3) | C3 | 1 | 3 | yes | maximal, complemented |
| 2 | C3×C9×C67 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C32×C67 | C32 | 1 | 1 | yes | characteristic |
| 4 | C3×C67⋊C3 | — | 3 | 3 | no | — |
| 5 | C9×C67 | — | 3 | 1 | no | — |
| 6 | C3×C67 | — | 3 | 1 | no | — |
| 7 | C3×C67 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 8 | C67⋊C3 | — | 9 | 3 | no | — |
| 9 | #732 | — | 67 | 1 | no | maximal, Sylow |
| 10 | C67 | #732 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | H(3,𝔽3) | — | 67 | 3 | no | — |
| 12 | C3×C9 | C67⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 13 | C32 | — | 201 | 3 | no | — |
| 14 | C32 | C3×C67⋊C3 | 1 | 1 | yes | characteristic |
| 15 | C9 | — | 3 | 1 | no | — |
| 16 | C3 | — | 3 | 1 | no | — |
| 17 | C3 | — | 603 | 3 | no | — |
| 18 | C3 | C32⋊(C67⋊C3) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C32⋊(C67⋊C3) |
| commutator | C32×C67 | C32 |
| Frattini | C32 | C3×C67⋊C3 |
| Fitting | C3×C9×C67 | C3 |
| socle | C3×C67 | H(3,𝔽3) |
| hypercenter | C3×C9 | C67⋊C3 |
| hypocenter | C67 | #732 |
| LCS | G ▷ C32×C67 ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ C3×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32⋊(C67⋊C3) | C3 | semidirect |
| 2. C3×C9×C67 | C3 | semidirect |
| 10. C67 | #732 | semidirect |
| 12. C3×C9 | C67⋊C3 | semidirect |