Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
612 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 170 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 | #2326 |
| 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×Q8×#64408 | C2 | semidirect |
| 3. (C2×#64408)⋊Q8 | C2 | semidirect |
| 5. #17989537 | C2 | semidirect |
| 6. #17989534 | C2 | semidirect |
| 7. #17989533 | C2 | semidirect |
| 8. #17989523 | C2 | semidirect |
| 27. #14556580 | C4 | semidirect |
| 28. #14556579 | C4 | semidirect |
| 29. #14556578 | C4 | semidirect |
| 30. #14556577 | C4 | semidirect |
| 33. #124×C73 | C4 | semidirect |
| 51. C2×Dic146 | C2×C4 | semidirect |
| 52. C2×Dic146 | C2×C4 | semidirect |
| 62. C22⋊Dic73 | C2×C4 | semidirect |
| 63. #11924005 | C2×C4 | semidirect |
| 64. #11924005 | C2×C4 | semidirect |
| 65. C4×Dic73 | C2×C4 | semidirect |
| 66. C4×Dic73 | C2×C4 | semidirect |
| 67. C2×Q8×C73 | C2×C4 | semidirect |
| 69. C22⋊C4×C73 | C2×C4 | semidirect |
| 70. C42×C73 | C2×C4 | semidirect |
| 139. C73 | #2326 | semidirect |
| 156. #124 | #64408 | semidirect |
| 178. C2×Q8 | C2×#64408 | semidirect |
| 203. C22⋊C4 | C2×#64408 | semidirect |
| 209. C42 | C2×#64408 | semidirect |