Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D113 |
| commutator | C4×C113 | C22×C4 |
| Frattini | C2×C4 | C22×D113 |
| Fitting | #104×C113 | C2 |
| socle | C2×C113 | C4×D4 |
| hypercenter | #104 | D113 |
| hypocenter | C113 | #444 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #104 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16813630 | C2 | semidirect |
| 3. #16813629 | C2 | semidirect |
| 4. #16813557 | C2 | semidirect |
| 5. #16813550 | C2 | semidirect |
| 6. #16813533 | C2 | semidirect |
| 7. #104×C113 | C2 | semidirect |
| 9. #14268637 | C4 | semidirect |
| 10. #14268635 | C4 | semidirect |
| 11. #14268634 | C4 | semidirect |
| 12. #14268632 | C4 | semidirect |
| 51. C113 | #444 | semidirect |
| 58. #104 | D113 | semidirect |