Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
560 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #124×C73 | C4 |
| hypercenter | #124 | #64408 |
| hypocenter | C73 | #2372 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. (C2×#64408)⋊Q8 | C2 | semidirect |
| 2. #17989537 | C2 | semidirect |
| 4. C22⋊C4×#64408 | C2 | semidirect |
| 5. #17989523 | C2 | semidirect |
| 19. #14556580 | C4 | semidirect |
| 20. #14556579 | C4 | semidirect |
| 21. #14556578 | C4 | semidirect |
| 22. #14556577 | C4 | semidirect |
| 25. #124×C73 | C4 | semidirect |
| 36. C2×Dic146 | C2×C4 | semidirect |
| 37. C2×Dic146 | C2×C4 | semidirect |
| 47. C22⋊Dic73 | C2×C4 | semidirect |
| 48. #11924005 | C2×C4 | semidirect |
| 49. #11924005 | C2×C4 | semidirect |
| 50. C4×Dic73 | C2×C4 | semidirect |
| 51. C4×Dic73 | C2×C4 | semidirect |
| 52. C2×Q8×C73 | C2×C4 | semidirect |
| 54. C22⋊C4×C73 | C2×C4 | semidirect |
| 55. C42×C73 | C2×C4 | semidirect |
| 113. C73 | #2372 | semidirect |
| 127. #124 | #64408 | semidirect |
| 144. C2×Q8 | C2×#64408 | semidirect |
| 163. C22⋊C4 | C2×#64408 | semidirect |
| 168. C42 | C2×#64408 | semidirect |