Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 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 | #121×C113 | C2 |
| hypercenter | #121 | D113 |
| hypocenter | C113 | #538 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813617 | C2 | semidirect |
| 2. #16813608 | C2 | semidirect |
| 3. #16813606 | C2 | semidirect |
| 4. #16813601 | C2 | semidirect |
| 5. #16813594 | C2 | semidirect |
| 6. #16813590 | C2 | semidirect |
| 7. D4×Dic113 | C2 | semidirect |
| 8. C2×#14268624 | C2 | semidirect |
| 9. #121×C113 | C2 | semidirect |
| 11. C2×Dic226 | C22 | semidirect |
| 15. C22×Dic113 | C22 | semidirect |
| 16. C4⋊Dic113 | C22 | semidirect |
| 17. C4⋊Dic113 | C22 | semidirect |
| 18. #14268626 | C22 | semidirect |
| 20. C22⋊Dic113 | C22 | semidirect |
| 25. C4×Dic113 | C22 | semidirect |
| 27. C2×D4×C113 | C22 | semidirect |
| 29. C4⋊C4×C113 | C22 | semidirect |
| 30. C22⋊C4×C113 | C22 | semidirect |
| 74. C113 | #538 | semidirect |
| 81. #121 | D113 | semidirect |
| 90. C2×D4 | C2×D113 | semidirect |
| 97. C4⋊C4 | C2×D113 | semidirect |
| 104. C22⋊C4 | C2×D113 | semidirect |