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 | #117×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | #117 | D113 |
| hypocenter | C113 | #520 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic226 | C2 | semidirect |
| 3. C4×D452 | C2 | semidirect |
| 4. #16813582 | C2 | semidirect |
| 5. #16813580 | C2 | semidirect |
| 6. C2×C4⋊Dic113 | C2 | semidirect |
| 7. C4⋊C4×D113 | C2 | semidirect |
| 8. #117×C113 | C2 | semidirect |
| 9. #14268647 | C4 | semidirect |
| 28. C2×C4×C113 | C2×C4 | semidirect |
| 33. C22⋊D113 | C2×C4 | semidirect |
| 37. D452 | C2×C4 | semidirect |
| 39. C4×D113 | C2×C4 | semidirect |
| 40. Dic226 | C2×C4 | semidirect |
| 59. C113 | #520 | semidirect |
| 66. #117 | D113 | semidirect |
| 96. C2×C4 | C4×D113 | semidirect |