Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×Dic78 | C2 | semidirect |
| 3. C3×C13×M16 | C2 | semidirect |
| 4. Dic156 | C2 | semidirect |
| 5. #10597658 | C2 | semidirect |
| 18. C13×M16 | D3 | semidirect |
| 48. C3×M16 | D13 | semidirect |
| 51. C3×C13 | #137 | semidirect |
| 69. M16 | D39 | semidirect |
| 70. C13 | #909 | semidirect |
| 95. C3 | #88163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597790 | 2 |
| C2×Dic78 | 2 |
| C3×C13×M16 | 2 |
| Dic156 | 2 |
| #10597658 | 2 |
| #88163 | 3 |
| #909 | 13 |