Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 | C4×D4×C113 | C2 |
| hypercenter | C4×D4 | D113 |
| hypocenter | C113 | D42 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D452 | C2 | semidirect |
| 2. C2×D4×D113 | C2 | semidirect |
| 3. #16813619 | C2 | semidirect |
| 4. #16813597 | C2 | semidirect |
| 5. #16813596 | C2 | semidirect |
| 6. #16813592 | C2 | semidirect |
| 7. C4×D452 | C2 | semidirect |
| 8. C4×D4×C113 | C2 | semidirect |
| 9. C23×D113 | C22 | semidirect |
| 12. C2×D452 | C22 | semidirect |
| 13. C2×D452 | C22 | semidirect |
| 14. C2×D452 | C22 | semidirect |
| 15. C2×D452 | C22 | semidirect |
| 16. C2×C22⋊D113 | C22 | semidirect |
| 18. C2×C4×D113 | C22 | semidirect |
| 19. C4⋊Dic113 | C22 | semidirect |
| 20. #14268624 | C22 | semidirect |
| 21. #14268624 | C22 | semidirect |
| 23. C22×C4×C113 | C22 | semidirect |
| 24. C4⋊C4×C113 | C22 | semidirect |
| 25. C22⋊C4×C113 | C22 | semidirect |
| 26. C42×C113 | C22 | semidirect |
| 33. D4×C113 | D4 | semidirect |
| 45. D452 | D4 | direct (N × H) |
| 49. C22×C113 | C2×D4 | semidirect |
| 57. C2×D113 | C2×D4 | semidirect |
| 60. C4×C113 | C2×D4 | semidirect |
| 61. C4×C113 | C2×D4 | semidirect |
| 69. C113 | D42 | semidirect |
| 78. C4×D4 | D113 | semidirect |
| 90. C22×C4 | C2×D113 | semidirect |
| 92. C4⋊C4 | C2×D113 | semidirect |
| 95. C22⋊C4 | C2×D113 | semidirect |
| 96. C42 | C2×D113 | semidirect |
| 109. D4 | D452 | direct (N × H) |
| 126. C22 | C2×D452 | semidirect |
| 131. C4 | D4×D113 | semidirect |
| 132. C4 | C2×D452 | semidirect |