Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D113 |
| commutator | C22×C113 | C24 |
| Frattini | C22 | C23×D113 |
| Fitting | C2×C4⋊C4×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C2×C4⋊C4 | D113 |
| hypocenter | C113 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic226 | C2 | semidirect |
| 3. #16813600 | C2 | direct (N × H) |
| 4. C2×#14268626 | C2 | semidirect |
| 5. C2×#14268626 | C2 | semidirect |
| 8. C2×C4⋊C4×C113 | C2 | semidirect |
| 11. C2×Dic226 | C22 | semidirect |
| 17. #14268626 | C22 | semidirect |
| 18. #14268626 | C22 | semidirect |
| 24. C4⋊C4×C113 | C22 | semidirect |
| 28. C22×D113 | Q8 | semidirect |
| 51. C2×D113 | C2×Q8 | semidirect |
| 58. C2×C113 | C22⋊Q8 | semidirect |
| 63. C113 | C2×C22⋊Q8 | semidirect |
| 70. C2×C4⋊C4 | D113 | semidirect |
| 86. C4⋊C4 | C2×D113 | semidirect |
| 123. C2 | #16813600 | direct (N × H) |