Finite Group DatabasebetaFinite Group DatabasebetaOrder 6084.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×C3×C169 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C169⋊C9 | — | 4 | 1 | no | maximal, Hall |
| 3 | C2×C3×C169 | — | 3 | 1 | no | — |
| 4 | C22×C169 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C3×C169 | A4 | 1 | 1 | yes | characteristic |
| 6 | C22⋊(C13⋊C9) | — | 13 | 1 | no | maximal |
| 7 | C2×C169 | — | 3 | 1 | no | — |
| 8 | C169 | C22⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C22×C3×C13 | C13⋊C3 | 1 | 1 | yes | characteristic |
| 10 | C13⋊C9 | — | 52 | 1 | no | — |
| 11 | C2×C3×C13 | — | 3 | 1 | no | — |
| 12 | C22×C13 | C13⋊C9 | 1 | 1 | yes | characteristic |
| 13 | C3×C13 | C22⋊(C13⋊C3) | 1 | 1 | yes | characteristic |
| 14 | C22⋊C9 | — | 169 | 1 | no | Hall |
| 15 | C2×C13 | — | 3 | 1 | no | — |
| 16 | C13 | C22⋊(C13⋊C9) | 1 | 1 | yes | characteristic |
| 17 | C22×C3 | C169⋊C3 | 1 | 1 | yes | characteristic |
| 18 | C9 | — | 676 | 1 | no | Sylow |
| 19 | C2×C3 | — | 3 | 1 | no | — |
| 20 | C22 | C169⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | C3 | C22⋊(C169⋊C3) | 1 | 1 | yes | characteristic |
| 22 | C2 | — | 3 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊(C169⋊C3) |
| commutator, hypocenter | C22×C169 | C9 |
| Frattini | C3×C13 | C22⋊(C13⋊C3) |
| Fitting | C22×C3×C169 | C3 |
| socle | C22×C3×C13 | C13⋊C3 |
| LCS | G ▷ C22×C169 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×C169 | C9 | semidirect |
| 8. C169 | C22⋊C9 | semidirect |
| 20. C22 | C169⋊C9 | semidirect |