Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #126×C113 | C2 |
| hypercenter | #126 | D113 |
| hypocenter | C113 | #560 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813619 | C2 | semidirect |
| 2. #16813616 | C2 | semidirect |
| 3. #16813607 | C2 | semidirect |
| 4. #16813597 | C2 | semidirect |
| 5. #16813595 | C2 | semidirect |
| 6. #16813592 | C2 | semidirect |
| 7. #126×C113 | C2 | semidirect |
| 11. C2×D452 | C22 | semidirect |
| 13. C2×C4×D113 | C22 | semidirect |
| 14. #14268626 | C22 | semidirect |
| 17. #14268624 | C22 | semidirect |
| 18. C4⋊C4×C113 | C22 | semidirect |
| 20. C42×C113 | C22 | semidirect |
| 50. C113 | #560 | semidirect |
| 54. #126 | D113 | semidirect |
| 66. C4⋊C4 | C2×D113 | semidirect |
| 71. C42 | C2×D113 | semidirect |