Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
652 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 182 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 | C4×#124 |
| 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. #17989531 | C2 | semidirect |
| 7. C22⋊C4×#64408 | C2 | semidirect |
| 8. C42×#64408 | C2 | semidirect |
| 27. #14556580 | C4 | semidirect |
| 28. #14556579 | C4 | semidirect |
| 29. #14556578 | C4 | semidirect |
| 30. #14556577 | C4 | semidirect |
| 33. #124×C73 | C4 | semidirect |
| 52. C2×Dic146 | C2×C4 | semidirect |
| 53. C2×Dic146 | C2×C4 | semidirect |
| 63. C22⋊Dic73 | C2×C4 | semidirect |
| 64. #11924005 | C2×C4 | semidirect |
| 65. #11924005 | C2×C4 | semidirect |
| 66. C4×Dic73 | C2×C4 | semidirect |
| 67. C4×Dic73 | C2×C4 | semidirect |
| 68. C2×Q8×C73 | C2×C4 | semidirect |
| 70. C22⋊C4×C73 | C2×C4 | semidirect |
| 71. C42×C73 | C2×C4 | semidirect |
| 125. #64408 | #124 | direct (N × H) |
| 140. C73 | C4×#124 | semidirect |
| 157. #124 | #64408 | direct (N × H) |
| 179. C2×Q8 | C2×#64408 | semidirect |
| 203. C22⋊C4 | C2×#64408 | semidirect |
| 211. C42 | C2×#64408 | semidirect |