Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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×C3×Q8×C13 | C2 | semidirect |
| 3. C13×#216 | C2 | semidirect |
| 4. C13×#215 | C2 | semidirect |
| 5. C13×#208 | C2 | semidirect |
| 17. C2×Q8×C13 | D3 | semidirect |
| 36. #942 | C13 | direct (N × H) |
| 46. C2×C3×Q8 | C2×C13 | semidirect |
| 48. #216 | C2×C13 | semidirect |
| 49. #215 | C2×C13 | semidirect |
| 50. #208 | C2×C13 | semidirect |
| 51. C3×C13 | #137 | semidirect |
| 66. C2×Q8 | D3×C13 | semidirect |
| 70. C13 | #942 | direct (N × H) |
| 95. C3 | C13×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C13 | 2 |
| C13×#235 | 2 |
| C13×#216 | 2 |
| C13×#215 | 2 |
| C13×#208 | 2 |
| C13×#137 | 3 |
| #942 | 13 |