Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
190 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 71 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 | C22×C113 | C22×C4 |
| Fitting | C2×C42×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C2×C42 | D113 |
| hypocenter | C113 | #388 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14268626 | C2 | semidirect |
| 5. #16813529 | C2 | semidirect |
| 6. #16813529 | C2 | semidirect |
| 7. C2×C42×C113 | C2 | semidirect |
| 15. #14268624 | C4 | semidirect |
| 74. C113 | #388 | semidirect |
| 80. C2×C42 | D113 | semidirect |