Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D113 |
| commutator | C4×C113 | C24 |
| Frattini | C4 | C23×D113 |
| Fitting | 2−1+4×C113 | C2 |
| socle | C2×C113 | C22×D4 |
| hypercenter | 2−1+4 | D113 |
| hypocenter | C113 | #578 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813669 | C2 | semidirect |
| 2. #16813653 | C2 | semidirect |
| 3. #16813652 | C2 | semidirect |
| 4. #16813642 | C2 | semidirect |
| 5. C2×#14268637 | C2 | semidirect |
| 6. #16813629 | C2 | semidirect |
| 7. 2−1+4×C113 | C2 | semidirect |
| 52. C113 | #578 | semidirect |
| 55. 2−1+4 | D113 | semidirect |