Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#14268631 | C2 | semidirect |
| 3. #16813550 | C2 | direct (N × H) |
| 4. C2×C42×C113 | C2 | semidirect |
| 7. #14268647 | C4 | semidirect |
| 9. C2×Dic226 | C4 | semidirect |
| 10. C2×D452 | C4 | semidirect |
| 14. #14268631 | C22 | semidirect |
| 19. C42×C113 | C22 | semidirect |
| 34. D452 | C2×C4 | semidirect |
| 38. Dic226 | C2×C4 | semidirect |
| 54. C2×C113 | #104 | semidirect |
| 57. C113 | C2×#104 | semidirect |
| 61. C2×C42 | D113 | semidirect |
| 77. C42 | C2×D113 | semidirect |
| 113. C2 | #16813550 | direct (N × H) |