Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #123×C113 | C2 |
| hypercenter | #123 | D113 |
| hypocenter | C113 | #551 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813615 | C2 | semidirect |
| 2. #16813609 | C2 | semidirect |
| 3. #16813604 | C2 | semidirect |
| 4. #16813600 | C2 | semidirect |
| 6. C4×C22⋊D113 | C2 | semidirect |
| 7. #16813580 | C2 | semidirect |
| 8. C22⋊C4×D113 | C2 | semidirect |
| 9. #123×C113 | C2 | semidirect |
| 11. C2×Dic226 | C22 | semidirect |
| 15. C4⋊Dic113 | C22 | semidirect |
| 16. #14268626 | C22 | semidirect |
| 17. #14268626 | C22 | semidirect |
| 20. C22⋊Dic113 | C22 | semidirect |
| 24. C4×Dic113 | C22 | semidirect |
| 25. C4×Dic113 | C22 | semidirect |
| 27. C22×C4×C113 | C22 | semidirect |
| 28. C4⋊C4×C113 | C22 | semidirect |
| 30. C22⋊C4×C113 | C22 | semidirect |
| 68. C113 | #551 | semidirect |
| 73. #123 | D113 | semidirect |
| 85. C22×C4 | C2×D113 | semidirect |
| 89. C4⋊C4 | C2×D113 | semidirect |
| 97. C22⋊C4 | C2×D113 | semidirect |