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 | C2×C22⋊C4×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | C2×C22⋊C4 | D113 |
| hypocenter | C113 | #518 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C22⋊D113 | C2 | semidirect |
| 3. #16813582 | C2 | semidirect |
| 4. #16813578 | C2 | semidirect |
| 5. C2×C22⋊Dic113 | C2 | semidirect |
| 6. C22⋊C4×D113 | C2 | semidirect |
| 7. C2×C22⋊C4×C113 | C2 | semidirect |
| 9. C2×C22⋊D113 | C4 | semidirect |
| 13. C22×Dic113 | C22 | semidirect |
| 14. C2×C4×D113 | C22 | semidirect |
| 15. #14268626 | C22 | semidirect |
| 17. C22⋊Dic113 | C22 | semidirect |
| 18. #14268624 | C22 | semidirect |
| 19. C4×Dic113 | C22 | semidirect |
| 21. C22×C4×C113 | C22 | semidirect |
| 23. C22⋊C4×C113 | C22 | semidirect |
| 25. C23×C113 | C2×C4 | semidirect |
| 30. C22×D113 | C2×C4 | semidirect |
| 34. C22⋊D113 | C2×C4 | semidirect |
| 35. C22⋊D113 | C2×C4 | semidirect |
| 37. C2×Dic113 | C2×C4 | semidirect |
| 61. C113 | #518 | semidirect |
| 69. C2×C22⋊C4 | D113 | semidirect |
| 78. C22×C4 | C2×D113 | semidirect |
| 84. C22⋊C4 | C2×D113 | semidirect |
| 90. C23 | C4×D113 | semidirect |