Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 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×C3×D52 | C2 | semidirect |
| 3. C2×C13×C3⋊C8 | C2 | semidirect |
| 4. #10597596 | C2 | direct (N × H) |
| 10. D156 | C22 | semidirect |
| 12. C3×D52 | C22 | semidirect |
| 13. C13×C3⋊C8 | C22 | semidirect |
| 15. C2×D52 | D3 | semidirect |
| 31. D52 | C2×D3 | semidirect |
| 34. C2×C3×C13 | D8 | semidirect |
| 48. C2×C3⋊C8 | D13 | semidirect |
| 49. C3×C13 | C2×D8 | semidirect |
| 51. C2×C13 | #213 | semidirect |
| 62. C3⋊C8 | C2×D13 | semidirect |
| 67. C13 | C2×#213 | semidirect |
| 84. C2×C3 | D104 | semidirect |
| 94. C3 | C2×D104 | semidirect |
| 97. C2 | #10597596 | 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×C3×D52 | 2 |
| C2×C13×C3⋊C8 | 2 |
| #10597596 | 2 |
| C2×D104 | 3 |
| C2×#213 | 13 |