Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
292 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#64408 |
| commutator | C22×C73 | C22×C8 |
| Fitting | C2×C22⋊C4×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C22⋊C4 | #64408 |
| hypocenter | C73 | #1923 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊#10596833 | C2 | semidirect |
| 4. C2×C4×#10596833 | C2 | semidirect |
| 5. #17989453 | C2 | semidirect |
| 6. #17989453 | C2 | semidirect |
| 53. C22⋊C4×C73 | C8 | semidirect |
| 123. C73 | #1923 | semidirect |
| 172. C22⋊C4 | #10596833 | semidirect |