Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C22×D4×C113 | C2 |
| hypercenter | C22×D4 | D113 |
| hypocenter | C113 | D42 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D113 | C2 | semidirect |
| 2. C2×D4×D113 | C2 | semidirect |
| 3. #16813618 | C2 | semidirect |
| 4. #16813596 | C2 | semidirect |
| 5. #16813594 | C2 | semidirect |
| 6. #16813593 | C2 | semidirect |
| 7. #16813591 | C2 | semidirect |
| 8. #16813590 | C2 | semidirect |
| 9. D4×Dic113 | C2 | semidirect |
| 10. C4×C22⋊D113 | C2 | semidirect |
| 11. C22×D4×C113 | C2 | semidirect |
| 12. C23×D113 | C22 | semidirect |
| 13. C2×D452 | C22 | semidirect |
| 16. C2×C22⋊D113 | C22 | semidirect |
| 17. C2×C22⋊D113 | C22 | semidirect |
| 18. C2×C22⋊D113 | C22 | semidirect |
| 19. C2×C22⋊D113 | C22 | semidirect |
| 20. C2×C22⋊D113 | C22 | semidirect |
| 22. C22×Dic113 | C22 | semidirect |
| 23. C2×C4×D113 | C22 | semidirect |
| 24. C4⋊Dic113 | C22 | semidirect |
| 25. #14268626 | C22 | semidirect |
| 26. C22⋊Dic113 | C22 | semidirect |
| 27. C22⋊Dic113 | C22 | semidirect |
| 28. C22⋊Dic113 | C22 | semidirect |
| 29. #14268624 | C22 | semidirect |
| 30. #14268624 | C22 | semidirect |
| 31. C4×Dic113 | C22 | semidirect |
| 32. C24×C113 | C22 | semidirect |
| 35. C2×D4×C113 | C22 | semidirect |
| 36. C2×D4×C113 | C22 | semidirect |
| 37. C22×C4×C113 | C22 | semidirect |
| 51. D4×C113 | D4 | semidirect |
| 60. C22⋊D113 | D4 | direct (N × H) |
| 76. C22×C113 | C2×D4 | semidirect |
| 77. C22×C113 | C2×D4 | semidirect |
| 85. C2×D113 | C2×D4 | semidirect |
| 87. C4×C113 | C2×D4 | semidirect |
| 91. Dic113 | C2×D4 | semidirect |
| 100. C113 | D42 | semidirect |
| 104. C22×D4 | D113 | semidirect |
| 114. C24 | C2×D113 | semidirect |
| 126. C2×D4 | C2×D113 | semidirect |
| 127. C2×D4 | C2×D113 | semidirect |
| 130. C22×C4 | C2×D113 | semidirect |
| 159. D4 | C22⋊D113 | direct (N × H) |
| 184. C22 | D4×D113 | semidirect |
| 185. C22 | C2×C22⋊D113 | semidirect |
| 192. C4 | C2×C22⋊D113 | semidirect |