Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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. #10597790 | C2 | semidirect |
| 2. C2×D156 | C2 | semidirect |
| 3. C3×C13×M16 | C2 | semidirect |
| 4. D312 | C2 | semidirect |
| 5. #10597658 | C2 | semidirect |
| 12. D156 | C22 | semidirect |
| 14. Dic78 | C22 | semidirect |
| 15. C3×C8×C13 | C22 | semidirect |
| 18. C13×M16 | D3 | semidirect |
| 36. C8×C13 | C2×D3 | semidirect |
| 51. C3×M16 | D13 | semidirect |
| 54. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 68. C3×C8 | C2×D13 | semidirect |
| 73. M16 | D39 | semidirect |
| 74. C13 | #908 | semidirect |
| 90. C8 | C2×D39 | semidirect |
| 102. C3 | #88162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597790 | 2 |
| C2×D156 | 2 |
| C3×C13×M16 | 2 |
| D312 | 2 |
| #10597658 | 2 |
| #88162 | 3 |
| #908 | 13 |