Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
372 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 150 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 | #125×C73 | C4 |
| hypercenter | #125 | #64408 |
| hypocenter | C73 | #2968 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989639 | C2 | semidirect |
| 2. #17989617 | C2 | semidirect |
| 3. #17989617 | C2 | semidirect |
| 4. #17989615 | C2 | semidirect |
| 5. #17989612 | C2 | semidirect |
| 6. #17989605 | C2 | semidirect |
| 7. #17989552 | C2 | semidirect |
| 8. #17989546 | C2 | semidirect |
| 112. C73 | #2968 | semidirect |