Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 3. #16813685 | C2 | direct (N × H) |
| 12. C2×Dic226 | C4 | semidirect |
| 15. Q8×D113 | C4 | semidirect |
| 19. C2×Q8×C113 | C4 | semidirect |
| 24. Q8×C113 | C2×C4 | semidirect |
| 38. Dic226 | C2×C4 | semidirect |
| 52. C2×C113 | #103 | semidirect |
| 54. D113 | #103 | semidirect |
| 57. C113 | C2×#103 | semidirect |
| 69. C2×Q8 | #90673 | semidirect |
| 84. Q8 | C2×#90673 | semidirect |
| 113. C2 | #16813685 | direct (N × H) |