Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #473×C73 | C2 |
| socle | C2×C73 | C2×#121 |
| hypercenter | #473 | D73 |
| hypocenter | C73 | #3067 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #473 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989386 | C2 | semidirect |
| 2. C2×#14556614 | C2 | semidirect |
| 3. #131×D73 | C2 | semidirect |
| 4. #17988859 | C2 | semidirect |
| 5. #17988858 | C2 | semidirect |
| 6. #17988857 | C2 | semidirect |
| 7. #17988853 | C2 | semidirect |
| 8. #17988852 | C2 | semidirect |
| 9. #108×D73 | C2 | semidirect |
| 10. #17988570 | C2 | semidirect |
| 11. #473×C73 | C2 | semidirect |
| 25. C2×#11924015 | C22 | semidirect |
| 26. C2×D584 | C22 | semidirect |
| 37. #14556527 | C22 | semidirect |
| 38. #14556526 | C22 | semidirect |
| 39. #14556510 | C22 | semidirect |
| 40. #14556507 | C22 | semidirect |
| 41. #14556507 | C22 | semidirect |
| 43. C2×Q16×C73 | C22 | semidirect |
| 45. #108×C73 | C22 | semidirect |
| 46. #101×C73 | C22 | semidirect |
| 167. C73 | #3067 | semidirect |
| 172. #473 | D73 | semidirect |
| 193. C2×Q16 | C2×D73 | semidirect |
| 209. #108 | C2×D73 | semidirect |
| 211. #101 | C2×D73 | semidirect |