Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
290 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 113 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, socle | C22×C113 | C24 |
| Fitting | C4×Q8×C113 | C2 |
| hypercenter | C4×Q8 | D113 |
| hypocenter | C113 | #548 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14268648 | C2 | semidirect |
| 2. C2×Q8×D113 | C2 | semidirect |
| 3. #16813610 | C2 | semidirect |
| 4. #16813602 | C2 | semidirect |
| 5. #16813597 | C2 | semidirect |
| 6. C4×D452 | C2 | semidirect |
| 7. C4×Q8×C113 | C2 | semidirect |
| 24. Q8×C113 | D4 | semidirect |
| 41. C2×D113 | #41 | semidirect |
| 52. C113 | #548 | semidirect |
| 59. C4×Q8 | D113 | semidirect |
| 78. Q8 | D452 | semidirect |