Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
| 4. C13×C4⋊Dic3 | C2 | semidirect |
| 5. C13×Dic3⋊C4 | C2 | semidirect |
| 14. C2×Q8×C13 | D3 | semidirect |
| 22. C2×D3×C13 | Q8 | semidirect |
| 34. #946 | C13 | direct (N × H) |
| 47. C2×C3×Q8 | C2×C13 | semidirect |
| 50. C4⋊Dic3 | C2×C13 | semidirect |
| 51. Dic3⋊C4 | C2×C13 | semidirect |
| 52. C3×C13 | C22⋊Q8 | semidirect |
| 65. C2×Q8 | D3×C13 | semidirect |
| 70. C13 | #946 | direct (N × H) |
| 74. C2×D3 | Q8×C13 | semidirect |
| 98. C3 | C13×C22⋊Q8 | 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 |
| C2×C4×D3×C13 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×C4⋊Dic3 | 2 |
| C13×Dic3⋊C4 | 2 |
| C13×C22⋊Q8 | 3 |
| #946 | 13 |