Finite Group DatabasebetaFinite Group DatabasebetaOrder 8172.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C9×C227 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Dic681 | — | 3 | 1 | no | maximal |
| 3 | C9×C227 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C2×C3×C227 | D3 | 1 | 1 | yes | characteristic |
| 5 | Dic227 | — | 9 | 1 | no | Hall |
| 6 | C3×C227 | Dic3 | 1 | 1 | yes | characteristic |
| 7 | C2×C227 | D9 | 1 | 1 | yes | characteristic |
| 8 | C227 | Dic9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | Dic9 | — | 227 | 1 | no | maximal, Hall |
| 10 | C2×C9 | D227 | 1 | 1 | yes | characteristic |
| 11 | Dic3 | — | 681 | 1 | no | — |
| 12 | C9 | Dic227 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C2×C3 | D681 | 1 | 1 | yes | characteristic |
| 14 | C4 | — | 2043 | 1 | no | Sylow |
| 15 | C3 | Dic681 | 1 | 1 | yes | characteristic |
| 16 | C2 | D2043 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2043 |
| commutator, hypocenter | C9×C227 | C4 |
| Frattini | C2×C3 | D681 |
| Fitting | C2×C9×C227 | C2 |
| socle | C2×C3×C227 | D3 |
| LCS | G ▷ C9×C227 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C9×C227 | C4 | semidirect |
| 8. C227 | Dic9 | semidirect |
| 12. C9 | Dic227 | semidirect |