Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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. C2×C3×Dic26 | C2 | semidirect |
| 4. C2×#64605 | C2 | semidirect |
| 6. D3×Dic26 | C2 | direct (N × H) |
| 11. Dic78 | C22 | semidirect |
| 15. C3×Dic26 | C22 | semidirect |
| 16. #64605 | C22 | semidirect |
| 23. C2×Dic26 | D3 | direct (N × H) |
| 25. C2×D3×C13 | Q8 | semidirect |
| 40. Dic26 | C2×D3 | direct (N × H) |
| 42. C2×C3×C13 | C2×Q8 | semidirect |
| 44. D3×C13 | C2×Q8 | semidirect |
| 58. C3×C13 | C22×Q8 | semidirect |
| 61. C2×C13 | D3×Q8 | semidirect |
| 79. C13 | C2×D3×Q8 | semidirect |
| 81. C2×D3 | Dic26 | direct (N × H) |
| 97. C2×C3 | C2×Dic26 | semidirect |
| 99. D3 | C2×Dic26 | direct (N × H) |
| 107. C3 | C22×Dic26 | semidirect |
| 109. C2 | D3×Dic26 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic78 | 2 |
| C2×C4×D3×C13 | 2 |
| C2×C3×Dic26 | 2 |
| C2×#64605 | 2 |
| C2×D3×Dic13 | 2 |
| D3×Dic26 | 2 |
| C22×Dic26 | 3 |
| C2×D3×Q8 | 13 |