Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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. C4×Dic39 | C2 | semidirect |
| 3. C3×#6101 | C2 | semidirect |
| 4. Dic3⋊Dic13 | C2 | semidirect |
| 5. #10597611 | C2 | semidirect |
| 21. #6101 | D3 | semidirect |
| 62. C3×C13 | #126 | semidirect |
| 82. C13 | #898 | semidirect |
| 114. C3 | #88133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic39 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C3×#6101 | 2 |
| Dic3⋊Dic13 | 2 |
| #10597611 | 2 |
| (C2×D3)⋊Dic13 | 2 |
| #88133 | 3 |
| #898 | 13 |