Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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 | C4×#41 |
| 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. #16813587 | C2 | semidirect |
| 3. #16813584 | C2 | semidirect |
| 4. #16813582 | C2 | semidirect |
| 5. #16813579 | C2 | semidirect |
| 6. C2×C4×Dic113 | C2 | semidirect |
| 7. C42×D113 | C2 | semidirect |
| 8. #117×C113 | C2 | semidirect |
| 9. #14268647 | C4 | semidirect |
| 28. C2×C4×C113 | C2×C4 | semidirect |
| 32. C22⋊D113 | C2×C4 | semidirect |
| 37. D452 | C2×C4 | semidirect |
| 39. C4×D113 | C2×C4 | semidirect |
| 40. Dic226 | C2×C4 | semidirect |
| 51. Dic113 | #41 | semidirect |
| 56. C113 | C4×#41 | semidirect |
| 63. #117 | D113 | semidirect |
| 94. C2×C4 | C4×D113 | semidirect |