Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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. C2×Dic78 | C2 | semidirect |
| 3. C3×#6099 | C2 | semidirect |
| 4. #10597606 | C2 | semidirect |
| 5. #10597602 | C2 | semidirect |
| 20. #6099 | D3 | semidirect |
| 51. C3×C13 | #137 | semidirect |
| 70. C13 | #909 | semidirect |
| 95. C3 | #88205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic78 | 2 |
| C13×#235 | 2 |
| C3×#6099 | 2 |
| #10597606 | 2 |
| #10597602 | 2 |
| #88205 | 3 |
| #909 | 13 |