Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #433×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #433 | D73 |
| hypocenter | C73 | #3222 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989199 | C2 | semidirect |
| 3. #17988981 | C2 | semidirect |
| 4. #17988960 | C2 | semidirect |
| 5. #17988952 | C2 | semidirect |
| 6. #17988942 | C2 | semidirect |
| 7. #17988810 | C2 | semidirect |
| 8. #17988788 | C2 | semidirect |
| 9. #17988751 | C2 | semidirect |
| 10. #17988740 | C2 | semidirect |
| 11. #433×C73 | C2 | semidirect |
| 14. C2×Dic292 | C22 | semidirect |
| 17. C2×#11924017 | C22 | semidirect |
| 18. #14556591 | C22 | semidirect |
| 22. #14556583 | C22 | semidirect |
| 29. C4×Dic146 | C22 | semidirect |
| 30. #14556516 | C22 | semidirect |
| 33. #14556513 | C22 | semidirect |
| 35. C4⋊C8×C73 | C22 | semidirect |
| 37. #97×C73 | C22 | semidirect |
| 38. C4×C8×C73 | C22 | semidirect |
| 123. C73 | #3222 | semidirect |
| 134. #433 | D73 | semidirect |
| 154. C4⋊C8 | C2×D73 | semidirect |
| 160. #97 | C2×D73 | semidirect |
| 161. C4×C8 | C2×D73 | semidirect |