Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 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 | C2×D4×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #474×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #474 | D73 |
| hypocenter | C73 | #3324 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #474 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989311 | C2 | semidirect |
| 3. #17988935 | C2 | semidirect |
| 4. #17988914 | C2 | semidirect |
| 5. #17988834 | C2 | semidirect |
| 6. #17988788 | C2 | semidirect |
| 7. #17988739 | C2 | semidirect |
| 8. C4×#11924016 | C2 | semidirect |
| 9. #17988664 | C2 | semidirect |
| 10. #17988590 | C2 | semidirect |
| 11. #474×C73 | C2 | semidirect |
| 14. C2×#11924017 | C22 | semidirect |
| 16. C2×#11924011 | C22 | semidirect |
| 20. #14556571 | C22 | semidirect |
| 25. C4×Dic146 | C22 | semidirect |
| 27. #14556549 | C22 | semidirect |
| 28. #14556522 | C22 | semidirect |
| 29. #14556514 | C22 | semidirect |
| 30. #14556513 | C22 | semidirect |
| 32. #14556511 | C22 | semidirect |
| 33. #14556511 | C22 | semidirect |
| 34. #14556503 | C22 | semidirect |
| 35. C4×#10596831 | C22 | semidirect |
| 36. C4⋊Q8×C73 | C22 | semidirect |
| 38. #107×C73 | C22 | semidirect |
| 39. C4⋊C8×C73 | C22 | semidirect |
| 136. C73 | #3324 | semidirect |
| 141. #474 | D73 | semidirect |
| 153. C4⋊Q8 | C2×D73 | semidirect |
| 166. #107 | C2×D73 | semidirect |
| 168. C4⋊C8 | C2×D73 | semidirect |