Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8×Dic113 | C2 | semidirect |
| 3. #16813556 | C2 | semidirect |
| 4. #16813546 | C2 | semidirect |
| 6. #16813532 | C2 | semidirect |
| 18. SD16×C113 | C4 | semidirect |
| 22. Q8×C113 | C2×C4 | semidirect |
| 32. C8×C113 | C2×C4 | semidirect |
| 49. C113 | #440 | semidirect |
| 61. SD16 | Dic113 | semidirect |
| 72. Q8 | C2×Dic113 | semidirect |
| 83. C8 | C2×Dic113 | semidirect |