Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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. M16×D113 | C2 | semidirect |
| 3. C42×D113 | C2 | semidirect |
| 4. #16813550 | C2 | semidirect |
| 5. #16813549 | C2 | semidirect |
| 6. #16813548 | C2 | semidirect |
| 7. #104×C113 | C2 | semidirect |
| 8. #14268648 | C4 | semidirect |
| 12. #14268646 | C4 | semidirect |
| 13. Q8×D113 | C4 | semidirect |
| 15. D4×D113 | C4 | semidirect |
| 19. #14268631 | C22 | semidirect |
| 23. C4×Dic113 | C22 | semidirect |
| 25. M16×C113 | C22 | semidirect |
| 26. C42×C113 | C22 | semidirect |
| 29. Q8×C113 | C2×C4 | semidirect |
| 31. D4×C113 | C2×C4 | semidirect |
| 42. D452 | C2×C4 | semidirect |
| 52. Dic226 | C2×C4 | semidirect |
| 75. D113 | #104 | direct (N × H) |
| 76. C113 | C2×#104 | semidirect |
| 84. #104 | D113 | direct (N × H) |
| 99. M16 | C2×D113 | semidirect |
| 103. C42 | C2×D113 | semidirect |
| 108. Q8 | C4×D113 | semidirect |
| 115. D4 | C4×D113 | semidirect |