Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#90673 |
| commutator | C4×C113 | C22×C4 |
| Frattini | C4 | C22×#90673 |
| Fitting | SD16×C113 | C4 |
| socle | C2×C113 | C4×D4 |
| hypercenter | SD16 | #90673 |
| hypocenter | C113 | #443 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813710 | C2 | semidirect |
| 2. #16813709 | C2 | semidirect |
| 3. #16813692 | C2 | semidirect |
| 4. #16813687 | C2 | semidirect |
| 5. #16813686 | C2 | semidirect |
| 6. C8×#90673 | C2 | semidirect |
| 18. #14268637 | C4 | semidirect |
| 19. #14268636 | C4 | semidirect |
| 20. #14268632 | C4 | semidirect |
| 22. SD16×C113 | C4 | semidirect |
| 51. C113 | #443 | semidirect |
| 64. SD16 | #90673 | semidirect |