Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
148 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 148 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 |
|---|---|---|
| 2. C2×C13×Dic6 | C2 | semidirect |
| 3. C3×C13×C4⋊C4 | C2 | semidirect |
| 6. C13×Dic3⋊C4 | C2 | semidirect |
| 7. C13×Dic3⋊C4 | C2 | semidirect |
| 22. C13×C4⋊C4 | D3 | semidirect |
| 28. C2×D3×C13 | Q8 | semidirect |
| 44. #896 | C13 | direct (N × H) |
| 60. C2×Dic6 | C2×C13 | semidirect |
| 61. C3×C4⋊C4 | C2×C13 | semidirect |
| 64. Dic3⋊C4 | C2×C13 | semidirect |
| 65. Dic3⋊C4 | C2×C13 | semidirect |
| 66. C3×C13 | C22⋊Q8 | semidirect |
| 85. C4⋊C4 | D3×C13 | semidirect |
| 88. C13 | #896 | direct (N × H) |
| 92. C2×D3 | Q8×C13 | semidirect |
| 122. 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×C4×D3×C13 | 2 |
| C2×C13×Dic6 | 2 |
| C3×C13×C4⋊C4 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×Dic3⋊C4 | 2 |
| C13×C22⋊Q8 | 3 |
| #896 | 13 |