Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 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. D113⋊M16 | C2 | semidirect |
| 2. C2×C4×#90673 | C2 | semidirect |
| 3. #16813687 | C2 | semidirect |
| 4. #16813686 | C2 | semidirect |
| 7. #14268657 | C22 | semidirect |
| 11. C4×#90673 | C22 | semidirect |
| 14. #14268647 | C4 | semidirect |
| 17. Q8×D113 | C4 | semidirect |
| 19. D4×D113 | C4 | semidirect |
| 22. #41×C113 | C4 | semidirect |
| 27. Q8×C113 | C2×C4 | semidirect |
| 29. D4×C113 | C2×C4 | semidirect |
| 38. D452 | C2×C4 | semidirect |
| 47. Dic226 | C2×C4 | semidirect |
| 68. D113 | #104 | semidirect |
| 69. C113 | C2×#104 | semidirect |
| 81. #41 | #90673 | semidirect |
| 97. Q8 | C2×#90673 | semidirect |
| 104. D4 | C2×#90673 | semidirect |