Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D113 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C22 | C23×D113 |
| Fitting | C4×D4×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | C4×D4 | D113 |
| hypocenter | C113 | C2×C4×D4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×D113 | C2 | semidirect |
| 3. C4×D452 | C2 | semidirect |
| 4. D4×Dic113 | C2 | semidirect |
| 5. #16813584 | C2 | semidirect |
| 6. C4×C22⋊D113 | C2 | semidirect |
| 7. #16813582 | C2 | semidirect |
| 8. C4⋊C4×D113 | C2 | semidirect |
| 9. C22⋊C4×D113 | C2 | semidirect |
| 10. C42×D113 | C2 | semidirect |
| 11. C4×D4×C113 | C2 | semidirect |
| 15. D4×D113 | C4 | direct (N × H) |
| 16. C22×Dic113 | C22 | semidirect |
| 22. C2×C4×D113 | C22 | semidirect |
| 23. C2×C4×D113 | C22 | semidirect |
| 24. C4⋊Dic113 | C22 | semidirect |
| 25. #14268626 | C22 | semidirect |
| 26. C22⋊Dic113 | C22 | semidirect |
| 27. #14268624 | C22 | semidirect |
| 28. #14268624 | C22 | semidirect |
| 29. C4×Dic113 | C22 | semidirect |
| 30. C4×Dic113 | C22 | semidirect |
| 31. C4×Dic113 | C22 | semidirect |
| 33. C22×C4×C113 | C22 | semidirect |
| 34. C4⋊C4×C113 | C22 | semidirect |
| 35. C22⋊C4×C113 | C22 | semidirect |
| 36. C42×C113 | C22 | semidirect |
| 40. C22×D113 | C2×C4 | semidirect |
| 43. D4×C113 | C2×C4 | semidirect |
| 49. C22⋊D113 | C2×C4 | semidirect |
| 55. D452 | C2×C4 | semidirect |
| 60. C4×D113 | C2×C4 | semidirect |
| 61. C4×D113 | D4 | direct (N × H) |
| 64. C22×C113 | C22×C4 | semidirect |
| 70. C2×D113 | C22×C4 | semidirect |
| 75. C4×C113 | C22×C4 | semidirect |
| 76. C4×C113 | C2×D4 | semidirect |
| 79. Dic113 | C22×C4 | semidirect |
| 80. Dic113 | C2×D4 | semidirect |
| 86. D113 | C4×D4 | direct (N × H) |
| 87. C113 | C2×C4×D4 | semidirect |
| 96. C4×D4 | D113 | direct (N × H) |
| 113. C22×C4 | C2×D113 | semidirect |
| 116. C4⋊C4 | C2×D113 | semidirect |
| 120. C22⋊C4 | C2×D113 | semidirect |
| 124. C42 | C2×D113 | semidirect |
| 133. D4 | C4×D113 | direct (N × H) |
| 159. C22 | C2×C4×D113 | semidirect |
| 167. C4 | C2×C4×D113 | semidirect |
| 168. C4 | D4×D113 | direct (N × H) |