Finite Group DatabasebetaFinite Group DatabasebetaOrder 9198.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×C9×C73 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C7×D219 | — | 3 | 1 | no | maximal |
| 3 | C3×C7×C73 | D3 | 1 | 1 | yes | characteristic |
| 4 | D657 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C7×D73 | — | 9 | 1 | no | Hall |
| 6 | C9×C73 | C2×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C7×C73 | D9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D219 | — | 3 | 1 | no | — |
| 9 | C3×C73 | D3×C7 | 1 | 1 | yes | characteristic |
| 10 | D73 | — | 9 | 1 | no | Hall |
| 11 | C7×D9 | — | 73 | 1 | no | maximal, Hall |
| 12 | C73 | C7×D9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C7×C9 | D73 | 1 | 1 | yes | characteristic, complemented, Hall |
| 14 | D3×C7 | — | 219 | 1 | no | — |
| 15 | C3×C7 | D219 | 1 | 1 | yes | characteristic |
| 16 | D9 | — | 73 | 1 | no | Hall |
| 17 | C2×C7 | — | 657 | 1 | no | Hall |
| 18 | C9 | C7×D73 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 19 | C7 | D657 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 20 | D3 | — | 219 | 1 | no | — |
| 21 | C3 | C7×D219 | 1 | 1 | yes | characteristic |
| 22 | C2 | — | 657 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D657 |
| commutator, hypocenter | C9×C73 | C2×C7 |
| Frattini | C3 | C7×D219 |
| Fitting | C7×C9×C73 | C2 |
| socle | C3×C7×C73 | D3 |
| LCS | G ▷ C9×C73 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×C9×C73 | C2 | semidirect |
| 4. D657 | C7 | direct (N × H) |
| 6. C9×C73 | C2×C7 | semidirect |
| 7. C7×C73 | D9 | semidirect |
| 12. C73 | C7×D9 | semidirect |
| 13. C7×C9 | D73 | semidirect |
| 18. C9 | C7×D73 | semidirect |
| 19. C7 | D657 | direct (N × H) |