Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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×Q8×C13⋊C3 | C2 | semidirect |
| 3. #6107⋊C3 | C2 | semidirect |
| 4. #6106⋊C3 | C2 | semidirect |
| 5. #6099⋊C3 | C2 | semidirect |
| 6. #88196 | C3 | semidirect |
| 16. C2×Q8×C13 | C2×C3 | semidirect |
| 18. #6107 | C2×C3 | semidirect |
| 19. #6106 | C2×C3 | semidirect |
| 20. #6099 | C2×C3 | semidirect |
| 51. C13⋊C3 | #137 | semidirect |
| 66. C2×Q8 | D13⋊C3 | semidirect |
| 70. C13 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C13⋊C3 | 2 |
| #6127⋊C3 | 2 |
| #6107⋊C3 | 2 |
| #6106⋊C3 | 2 |
| #6099⋊C3 | 2 |
| #88196 | 3 |
| C3×#137 | 13 |