Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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×D113 |
| commutator, socle | C22×C113 | C24 |
| Fitting | #125×C113 | C2 |
| hypercenter | #125 | D113 |
| hypocenter | C113 | #529 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813617 | C2 | semidirect |
| 2. #16813610 | C2 | semidirect |
| 3. #16813607 | C2 | semidirect |
| 4. #16813602 | C2 | semidirect |
| 6. #16813587 | C2 | semidirect |
| 7. #16813584 | C2 | semidirect |
| 8. #16813584 | C2 | semidirect |
| 9. #16813580 | C2 | semidirect |
| 10. C42×D113 | C2 | semidirect |
| 11. #125×C113 | C2 | semidirect |
| 74. C113 | #529 | semidirect |
| 77. #125 | D113 | semidirect |