Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D292 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #431×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #431 | D73 |
| hypocenter | C73 | #3211 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989121 | C2 | semidirect |
| 2. C2×#14556579 | C2 | semidirect |
| 3. #17988971 | C2 | semidirect |
| 4. #17988942 | C2 | semidirect |
| 5. #17988810 | C2 | semidirect |
| 6. #17988803 | C2 | semidirect |
| 7. #17988745 | C2 | semidirect |
| 8. #17988740 | C2 | semidirect |
| 9. #17988728 | C2 | semidirect |
| 11. #431×C73 | C2 | semidirect |
| 14. C2×Dic292 | C22 | semidirect |
| 16. C2×#11924017 | C22 | semidirect |
| 19. #14556583 | C22 | semidirect |
| 24. #14556579 | C22 | semidirect |
| 28. C4×Dic146 | C22 | semidirect |
| 29. C4×D292 | C22 | semidirect |
| 34. #14556516 | C22 | semidirect |
| 35. #14556516 | C22 | semidirect |
| 39. C4⋊C8×C73 | C22 | semidirect |
| 42. C4×C8×C73 | C22 | semidirect |
| 144. C73 | #3211 | semidirect |
| 155. #431 | D73 | semidirect |
| 179. C4⋊C8 | C2×D73 | semidirect |
| 186. C4×C8 | C2×D73 | semidirect |