Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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 | #117×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | #117 | D113 |
| hypocenter | C113 | C2×#117 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16813581 | C2 | semidirect |
| 3. #16813580 | C2 | semidirect |
| 4. #16813579 | C2 | semidirect |
| 5. #16813578 | C2 | semidirect |
| 6. C4⋊C4×D113 | C2 | semidirect |
| 8. C42×D113 | C2 | semidirect |
| 9. #117×C113 | C2 | semidirect |
| 12. C2×C4×D113 | C4 | semidirect |
| 18. C4⋊Dic113 | C22 | semidirect |
| 19. #14268626 | C22 | semidirect |
| 22. C4×Dic113 | C22 | semidirect |
| 23. C4×Dic113 | C22 | semidirect |
| 25. C4⋊C4×C113 | C22 | semidirect |
| 27. C42×C113 | C22 | semidirect |
| 33. C2×C4×C113 | C2×C4 | semidirect |
| 37. C2×Dic113 | C2×C4 | semidirect |
| 44. C4×D113 | C2×C4 | semidirect |
| 45. C4×D113 | C2×C4 | semidirect |
| 64. D113 | #117 | direct (N × H) |
| 65. C113 | C2×#117 | semidirect |
| 72. #117 | D113 | direct (N × H) |
| 87. C4⋊C4 | C2×D113 | semidirect |
| 93. C42 | C2×D113 | semidirect |
| 108. C2×C4 | C4×D113 | semidirect |