Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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. #16813553 | C2 | semidirect |
| 4. #16813546 | C2 | semidirect |
| 6. C4×#11744751 | C2 | semidirect |
| 7. C4×Q8×C113 | C2 | semidirect |
| 10. #14268634 | C4 | direct (N × H) |
| 22. Q8×C113 | C2×C4 | semidirect |
| 33. #11744751 | C2×C4 | semidirect |
| 41. C4×C113 | SD16 | semidirect |
| 49. C113 | C4×SD16 | semidirect |
| 52. C4×Q8 | D113 | semidirect |
| 72. Q8 | C4×D113 | semidirect |
| 92. C4 | #14268634 | direct (N × H) |