Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
184 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 84 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. C4⋊Dic39 | C2 | semidirect |
| 4. C3×C4⋊Dic13 | C2 | semidirect |
| 5. Dic3⋊Dic13 | C2 | semidirect |
| 11. C4×D3×C13 | C4 | semidirect |
| 18. C4⋊Dic13 | D3 | direct (N × H) |
| 23. C3×C4×C13 | C2×C4 | semidirect |
| 26. Dic3×C13 | C2×C4 | semidirect |
| 38. D3×C13 | C4⋊C4 | semidirect |
| 44. C4×C13 | C4×D3 | semidirect |
| 52. C3×C13 | C2×C4⋊C4 | semidirect |
| 64. C4×D3 | Dic13 | semidirect |
| 70. C13 | D3×C4⋊C4 | semidirect |
| 76. C3×C4 | C2×Dic13 | semidirect |
| 78. Dic3 | C2×Dic13 | semidirect |
| 89. D3 | C4⋊Dic13 | direct (N × H) |
| 97. C4 | D3×Dic13 | semidirect |
| 98. C3 | C2×C4⋊Dic13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C13 | 2 |
| C2×D3×Dic13 | 2 |
| C4⋊Dic39 | 2 |
| C3×C4⋊Dic13 | 2 |
| Dic3⋊Dic13 | 2 |
| C2×C4⋊Dic13 | 3 |
| D3×C4⋊C4 | 13 |