Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D292 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #443×C73 | C2 |
| socle | C2×C73 | D42 |
| hypercenter | #443 | D73 |
| hypocenter | C73 | #3290 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989401 | C2 | semidirect |
| 2. #17989399 | C2 | semidirect |
| 3. #17989389 | C2 | semidirect |
| 4. #17988971 | C2 | semidirect |
| 5. #17988863 | C2 | semidirect |
| 6. #17988858 | C2 | semidirect |
| 7. #17988850 | C2 | semidirect |
| 8. #17988766 | C2 | semidirect |
| 9. #17988761 | C2 | semidirect |
| 10. #17988705 | C2 | semidirect |
| 11. #443×C73 | C2 | semidirect |
| 12. #14556638 | C22 | semidirect |
| 16. #14556621 | C22 | semidirect |
| 19. #14556619 | C22 | semidirect |
| 26. C2×Dic292 | C22 | semidirect |
| 29. C2×#11924017 | C22 | semidirect |
| 33. #14556597 | C22 | semidirect |
| 34. #14556579 | C22 | semidirect |
| 35. #14556527 | C22 | semidirect |
| 37. #14556519 | C22 | semidirect |
| 38. #14556509 | C22 | semidirect |
| 39. #14556507 | C22 | semidirect |
| 41. #131×C73 | C22 | semidirect |
| 42. #108×C73 | C22 | semidirect |
| 43. #104×C73 | C22 | semidirect |
| 44. C4×C8×C73 | C22 | semidirect |
| 150. C73 | #3290 | semidirect |
| 161. #443 | D73 | semidirect |
| 185. #131 | C2×D73 | semidirect |
| 188. #108 | C2×D73 | semidirect |
| 191. #104 | C2×D73 | semidirect |
| 194. C4×C8 | C2×D73 | semidirect |