Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D113 |
| commutator, socle | C23×C113 | C23 |
| Fitting | C2×C4⋊C4×C113 | C2 |
| hypercenter | C2×C4⋊C4 | D113 |
| hypocenter | C113 | #399 |
| LCS | G ▷ C23×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14268626 | C2 | semidirect |
| 4. #16813529 | C2 | semidirect |
| 5. C2×C4⋊C4×C113 | C2 | semidirect |
| 51. C113 | #399 | semidirect |
| 54. C2×C4⋊C4 | D113 | semidirect |