Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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 | #461×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #461 | D73 |
| hypocenter | C73 | #3036 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556618 | C2 | semidirect |
| 2. #17989138 | C2 | semidirect |
| 3. C4×D4×D73 | C2 | semidirect |
| 4. #17988805 | C2 | semidirect |
| 5. #17988804 | C2 | semidirect |
| 6. #17988789 | C2 | semidirect |
| 7. #17988783 | C2 | semidirect |
| 8. #17988782 | C2 | semidirect |
| 9. #17988609 | C2 | semidirect |
| 10. #17988587 | C2 | semidirect |
| 11. #461×C73 | C2 | semidirect |
| 20. #14556588 | C22 | semidirect |
| 21. #14556580 | C22 | semidirect |
| 34. C4⋊#10596831 | C22 | semidirect |
| 35. #14556520 | C22 | semidirect |
| 36. #14556515 | C22 | semidirect |
| 37. #14556513 | C22 | semidirect |
| 38. #14556511 | C22 | semidirect |
| 40. C4⋊Q8×C73 | C22 | semidirect |
| 42. C4⋊C8×C73 | C22 | semidirect |
| 43. #103×C73 | C22 | semidirect |
| 54. D4×D73 | D4 | semidirect |
| 146. C4×C73 | AGL(1,ℤ/8) | semidirect |
| 161. C73 | #3036 | semidirect |
| 168. #461 | D73 | semidirect |
| 182. C4⋊Q8 | C2×D73 | semidirect |
| 200. C4⋊C8 | C2×D73 | semidirect |
| 202. #103 | C2×D73 | semidirect |
| 311. C4 | #14556618 | semidirect |