Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 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×D156 | C2 | semidirect |
| 2. C2×C4×D3×C13 | C2 | semidirect |
| 3. C2×C3×Dic26 | C2 | semidirect |
| 4. C2×#64604 | C2 | semidirect |
| 5. C2×#64601 | C2 | semidirect |
| 6. #10597735 | C2 | direct (N × H) |
| 11. D156 | C22 | semidirect |
| 13. C4×D3×C13 | C22 | semidirect |
| 15. C3×Dic26 | C22 | semidirect |
| 16. #64604 | C22 | semidirect |
| 17. #64601 | C22 | semidirect |
| 23. C2×Dic26 | D3 | semidirect |
| 41. Dic26 | C2×D3 | semidirect |
| 43. C2×C3×C13 | #41 | semidirect |
| 60. C2×C4×D3 | D13 | semidirect |
| 61. C3×C13 | C2×#41 | semidirect |
| 64. C2×C13 | #239 | semidirect |
| 76. C4×D3 | C2×D13 | semidirect |
| 83. C13 | C2×#239 | semidirect |
| 102. C2×C3 | #6127 | semidirect |
| 114. C3 | C2×#6127 | semidirect |
| 117. C2 | #10597735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D156 | 2 |
| C2×C4×D3×C13 | 2 |
| C2×C3×Dic26 | 2 |
| C2×#64604 | 2 |
| C2×#64601 | 2 |
| #10597735 | 2 |
| C2×#6127 | 3 |
| C2×#239 | 13 |