Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 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. #10597664 | C2 | semidirect |
| 4. C3×C4×Dic13 | C2 | semidirect |
| 5. #10597612 | C2 | semidirect |
| 7. Dic3×Dic13 | C2 | semidirect |
| 16. D3×Dic13 | C4 | semidirect |
| 23. C4×Dic13 | D3 | semidirect |
| 64. C3×C13 | #117 | semidirect |
| 85. C13 | #872 | semidirect |
| 118. C3 | #88131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic13 | 2 |
| #10597664 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C3×C4×Dic13 | 2 |
| #10597612 | 2 |
| (C2×D3)⋊Dic13 | 2 |
| Dic3×Dic13 | 2 |
| #88131 | 3 |
| #872 | 13 |