Finite Group DatabasebetaFinite Group DatabasebetaOrder 5427.
34 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C67⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C67⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×C67⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×C9×C67 | C3 | 1 | 1 | yes | maximal, characteristic |
| 5 | C32×C67 | C32 | 1 | 1 | yes | characteristic |
| 6 | C9×C67 | — | 3 | 1 | no | — |
| 7 | C67⋊C9 | — | 3 | 1 | no | — |
| 8 | C67⋊C9 | — | 3 | 1 | no | — |
| 9 | C67⋊C9 | C9 | 1 | 3 | yes | complemented |
| 10 | C3×C67 | C3×C9 | 1 | 1 | yes | characteristic |
| 11 | C3×C67 | 3−1+2 | 1 | 1 | yes | characteristic |
| 12 | C3×C67 | 3−1+2 | 1 | 1 | yes | characteristic |
| 13 | C3×C67 | 3−1+2 | 1 | 1 | yes | characteristic |
| 14 | C9⋊C9 | — | 67 | 1 | no | maximal, Sylow |
| 15 | C67 | C9⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C3×C9 | — | 67 | 1 | no | — |
| 17 | C3×C9 | — | 67 | 1 | no | — |
| 18 | C3×C9 | — | 67 | 1 | no | — |
| 19 | C3×C9 | C67⋊C3 | 1 | 1 | yes | characteristic |
| 20 | C32 | C3×C67⋊C3 | 1 | 1 | yes | characteristic |
| 21 | C9 | — | 3 | 1 | no | — |
| 22 | C9 | — | 67 | 3 | no | — |
| 23 | C9 | — | 201 | 1 | no | — |
| 24 | C9 | — | 201 | 1 | no | — |
| 25 | C3 | C9×C67⋊C3 | 1 | 1 | yes | characteristic |
| 26 | C3 | #14268671 | 1 | 1 | yes | characteristic |
| 27 | C3 | #14268672 | 1 | 1 | yes | characteristic |
| 28 | C3 | #14268673 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C67⋊C3 |
| commutator | C3×C67 | C3×C9 |
| Fitting | C3×C9×C67 | C3 |
| socle | C32×C67 | C32 |
| hypercenter | C3×C9 | C67⋊C3 |
| hypocenter | C67 | C9⋊C9 |
| LCS | G ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C32 ◁ C3×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C67⋊C9 | C9 | semidirect |
| 15. C67 | C9⋊C9 | semidirect |