Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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 | C2×C113 | C23×C4 |
| Fitting | C4×D4×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | C4×D4 | D113 |
| hypocenter | C113 | #518 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D452 | C2 | semidirect |
| 3. D4×Dic113 | C2 | semidirect |
| 4. #16813584 | C2 | semidirect |
| 5. C4×C22⋊D113 | C2 | semidirect |
| 6. #16813582 | C2 | semidirect |
| 7. #16813580 | C2 | semidirect |
| 8. #16813579 | C2 | semidirect |
| 9. C2×#14268624 | C2 | semidirect |
| 10. C22⋊C4×D113 | C2 | semidirect |
| 11. C4×D4×C113 | C2 | semidirect |
| 15. D4×D113 | C4 | semidirect |
| 16. C22×Dic113 | C22 | semidirect |
| 18. C2×C4×D113 | C22 | semidirect |
| 19. C2×C4×D113 | C22 | semidirect |
| 20. C4⋊Dic113 | C22 | semidirect |
| 21. #14268626 | C22 | semidirect |
| 22. #14268626 | C22 | semidirect |
| 23. C22⋊Dic113 | C22 | semidirect |
| 27. #14268624 | C22 | semidirect |
| 28. #14268624 | C22 | semidirect |
| 29. C4×Dic113 | C22 | semidirect |
| 30. C4×Dic113 | C22 | semidirect |
| 32. C22×C4×C113 | C22 | semidirect |
| 33. C4⋊C4×C113 | C22 | semidirect |
| 34. C22⋊C4×C113 | C22 | semidirect |
| 35. C42×C113 | C22 | semidirect |
| 39. C22×D113 | C2×C4 | semidirect |
| 42. D4×C113 | C2×C4 | semidirect |
| 48. C22⋊D113 | C2×C4 | semidirect |
| 54. D452 | C2×C4 | semidirect |
| 57. C4×D113 | C2×C4 | semidirect |
| 83. C113 | #518 | semidirect |
| 91. C4×D4 | D113 | semidirect |
| 105. C22×C4 | C2×D113 | semidirect |
| 109. C4⋊C4 | C2×D113 | semidirect |
| 116. C22⋊C4 | C2×D113 | semidirect |
| 119. C42 | C2×D113 | semidirect |
| 128. D4 | C4×D113 | semidirect |