Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17989535 |
| commutator | C23×C73 | C22×C4 |
| Frattini | C23 | C22×#64408 |
| Fitting | #123×C73 | C4 |
| socle | C2×C73 | #386 |
| hypercenter | #123 | #64408 |
| hypocenter | C73 | #1913 |
| LCS | G ▷ C23×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989654 | C2 | semidirect |
| 2. C2×#14556650 | C2 | semidirect |
| 3. D73⋊#99 | C2 | semidirect |
| 4. #17989464 | C2 | semidirect |
| 17. #14556574 | C4 | semidirect |
| 21. #14556561 | C4 | semidirect |
| 22. #14556559 | C4 | semidirect |
| 24. #123×C73 | C4 | semidirect |
| 33. C22⋊#64408 | D4 | semidirect |
| 35. C23×D73 | C2×C4 | semidirect |
| 52. C22⋊Dic73 | C2×C4 | semidirect |
| 58. C22×C4×C73 | C2×C4 | semidirect |
| 61. C22⋊C4×C73 | C2×C4 | semidirect |
| 136. C73 | #1913 | semidirect |
| 146. #123 | #64408 | semidirect |
| 181. C22×C4 | C2×#64408 | semidirect |
| 196. C22⋊C4 | C2×#64408 | semidirect |