Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #16813653 | C2 | direct (N × H) |
| 3. C2×#14268637 | C2 | semidirect |
| 4. C2×#14268634 | C2 | semidirect |
| 5. C2×#14268631 | C2 | semidirect |
| 6. C22×Q8×C113 | C2 | semidirect |
| 13. #14268637 | C22 | semidirect |
| 14. #14268634 | C22 | semidirect |
| 15. #14268631 | C22 | semidirect |
| 20. C2×Q8×C113 | C22 | semidirect |
| 53. C2×C113 | #137 | semidirect |
| 56. C113 | C2×#137 | semidirect |
| 59. C22×Q8 | D113 | semidirect |
| 70. C2×Q8 | C2×D113 | semidirect |
| 111. C2 | #16813653 | direct (N × H) |