Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 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×C22⋊C4×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C2×C22⋊C4 | D113 |
| hypocenter | C113 | C2×#120 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D113 | C2 | semidirect |
| 2. C22×D452 | C2 | semidirect |
| 3. C22×C22⋊D113 | C2 | semidirect |
| 4. #16813592 | C2 | direct (N × H) |
| 5. C2×#14268624 | C2 | semidirect |
| 6. C2×C22⋊C4×C113 | C2 | semidirect |
| 10. C23×D113 | C22 | semidirect |
| 11. C23×D113 | C22 | semidirect |
| 13. C2×D452 | C22 | semidirect |
| 15. C2×C22⋊D113 | C22 | semidirect |
| 16. C22×Dic113 | C22 | semidirect |
| 17. #14268624 | C22 | semidirect |
| 19. C22×C4×C113 | C22 | semidirect |
| 20. C22⋊C4×C113 | C22 | semidirect |
| 22. C23×C113 | D4 | semidirect |
| 32. C22×D113 | D4 | semidirect |
| 34. C22×D113 | C23 | semidirect |
| 36. C2×C4×C113 | C23 | semidirect |
| 39. C2×Dic113 | C23 | semidirect |
| 45. C22×C113 | C2×D4 | semidirect |
| 54. C2×D113 | C2×D4 | semidirect |
| 58. C2×C113 | #120 | semidirect |
| 63. C113 | C2×#120 | semidirect |
| 70. C2×C22⋊C4 | D113 | semidirect |
| 82. C22×C4 | C2×D113 | semidirect |
| 84. C22⋊C4 | C2×D113 | semidirect |
| 96. C23 | D452 | semidirect |
| 104. C2×C4 | C22×D113 | semidirect |
| 117. C22 | C2×D452 | semidirect |
| 124. C2 | #16813592 | direct (N × H) |