Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 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 | #520 |
| 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×Dic226 | C2 | semidirect |
| 3. #16813587 | C2 | semidirect |
| 4. D4×Dic113 | C2 | semidirect |
| 5. C4×C22⋊D113 | C2 | semidirect |
| 6. #16813582 | C2 | semidirect |
| 7. #16813579 | C2 | semidirect |
| 8. #16813578 | C2 | semidirect |
| 9. C2×#14268626 | C2 | semidirect |
| 10. C4⋊C4×D113 | C2 | semidirect |
| 11. C4×D4×C113 | C2 | semidirect |
| 12. #14268646 | C4 | semidirect |
| 38. D4×C113 | C2×C4 | semidirect |
| 44. C22⋊D113 | C2×C4 | semidirect |
| 46. C2×Dic113 | C2×C4 | semidirect |
| 53. C4×D113 | C2×C4 | semidirect |
| 54. Dic226 | C2×C4 | semidirect |
| 76. C113 | #520 | semidirect |
| 84. C4×D4 | D113 | semidirect |
| 117. D4 | C4×D113 | semidirect |