Finite Group DatabasebetaFinite Group DatabasebetaOrder 9198.
24 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #17987164 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | (C73⋊C3)⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C7×C73⋊C3 | C2×C3 | 1 | 1 | yes | characteristic |
| 4 | #10620323⋊C2 | — | 7 | 1 | no | maximal, Hall |
| 5 | D511 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | #10620323 | — | 7 | 1 | no | Hall |
| 7 | C7×C73 | C2×C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D73⋊C3 | — | 7 | 1 | no | — |
| 9 | C73⋊C3 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 10 | D73 | — | 7 | 1 | no | Hall |
| 11 | D7⋊C9 | — | 73 | 1 | no | maximal, Hall |
| 12 | C73 | D7⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C7⋊C9 | — | 73 | 1 | no | Hall |
| 14 | C3×D7 | — | 73 | 1 | no | — |
| 15 | C3×C7 | — | 73 | 1 | no | — |
| 16 | C2×C9 | — | 511 | 1 | no | Hall |
| 17 | D7 | — | 73 | 1 | no | Hall |
| 18 | C9 | — | 511 | 1 | no | Sylow |
| 19 | C7 | #10620323⋊C2 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 20 | C2×C3 | — | 511 | 1 | no | — |
| 21 | C3 | — | 73 | 1 | no | — |
| 22 | C2 | — | 511 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C73 | C2×C9 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17987164 | C2 | semidirect |
| 5. D511 | C9 | semidirect |
| 7. C7×C73 | C2×C9 | semidirect |
| 12. C73 | D7⋊C9 | semidirect |
| 19. C7 | #10620323⋊C2 | semidirect |