Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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. C22×C3×C4×C13 | C2 | semidirect |
| 3. C13×#217 | C2 | semidirect |
| 4. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C13×Dic3⋊C4 | C2 | semidirect |
| 15. C22×C4×C13 | D3 | semidirect |
| 34. #929 | C13 | direct (N × H) |
| 47. C22×C3×C4 | C2×C13 | semidirect |
| 49. #217 | C2×C13 | semidirect |
| 50. (C2×D3)⋊C4 | C2×C13 | semidirect |
| 51. Dic3⋊C4 | C2×C13 | semidirect |
| 52. C3×C13 | #123 | semidirect |
| 66. C22×C4 | D3×C13 | semidirect |
| 70. C13 | #929 | direct (N × H) |
| 98. C3 | C13×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C13 | 2 |
| C2×C13×#67 | 2 |
| C13×#217 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×Dic3⋊C4 | 2 |
| C13×#123 | 3 |
| #929 | 13 |