Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #120×C73 | C4 |
| hypercenter | #120 | #64408 |
| hypocenter | C73 | #2375 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989539 | C2 | semidirect |
| 2. #17989537 | C2 | semidirect |
| 3. #17989535 | C2 | semidirect |
| 4. #17989528 | C2 | semidirect |
| 6. C23×#64408 | C22 | semidirect |
| 7. C2×C4⋊#64408 | C22 | semidirect |
| 10. C2×C22⋊#64408 | C22 | semidirect |
| 11. C2×C4×#64408 | C22 | semidirect |
| 12. (C2×#64408)⋊C4 | C22 | semidirect |
| 15. #14556561 | C4 | semidirect |
| 16. #14556560 | C4 | semidirect |
| 17. #14556559 | C4 | semidirect |
| 19. #120×C73 | C4 | semidirect |
| 30. C23×D73 | C2×C4 | semidirect |
| 39. C22⋊Dic73 | C2×C4 | semidirect |
| 40. #11924005 | C2×C4 | semidirect |
| 41. C24×C73 | C2×C4 | semidirect |
| 43. C22⋊C4×C73 | C2×C4 | semidirect |
| 101. C73 | #2375 | semidirect |
| 113. #120 | #64408 | semidirect |
| 126. C24 | C2×#64408 | semidirect |
| 143. C22⋊C4 | C2×#64408 | semidirect |