Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813668 | C2 | semidirect |
| 2. #16813648 | C2 | semidirect |
| 3. #16813647 | C2 | semidirect |
| 4. #16813642 | C2 | semidirect |
| 5. C2×#14268632 | C2 | semidirect |
| 6. #16813629 | C2 | semidirect |
| 7. H(5,𝔽2)×C113 | C2 | semidirect |
| 9. #14268647 | C22 | semidirect |
| 10. C2×D452 | C22 | semidirect |
| 12. #14268637 | C22 | semidirect |
| 13. #14268635 | C22 | semidirect |
| 14. #14268634 | C22 | semidirect |
| 15. #14268632 | C22 | semidirect |
| 16. #14268632 | C22 | semidirect |
| 17. #14268631 | C22 | semidirect |
| 18. C2×#11744751 | C22 | semidirect |
| 21. #41×C113 | C22 | semidirect |
| 23. C2×D4×C113 | C22 | semidirect |
| 54. C113 | #576 | semidirect |
| 57. H(5,𝔽2) | D113 | semidirect |
| 67. #41 | C2×D113 | semidirect |
| 71. C2×D4 | C2×D113 | semidirect |