Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
290 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C22×Q8×C113 | C2 |
| hypercenter | C22×Q8 | D113 |
| hypocenter | C113 | #548 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14268648 | C2 | semidirect |
| 2. #16813611 | C2 | semidirect |
| 3. #16813598 | C2 | semidirect |
| 4. #16813596 | C2 | semidirect |
| 5. Q8×Dic113 | C2 | semidirect |
| 6. C4×C22⋊D113 | C2 | semidirect |
| 7. C22×Q8×C113 | C2 | semidirect |
| 25. Q8×C113 | D4 | semidirect |
| 37. C22×C113 | #41 | semidirect |
| 52. C113 | #548 | semidirect |
| 55. C22×Q8 | D113 | semidirect |
| 78. Q8 | C22⋊D113 | semidirect |
| 93. C22 | #14268648 | semidirect |