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 |
|---|---|---|
| 3. #10597670 | C2 | semidirect |
| 4. C3×#6107 | C2 | semidirect |
| 5. #10597606 | C2 | semidirect |
| 6. #10597604 | C2 | semidirect |
| 25. #6107 | D3 | direct (N × H) |
| 47. D3×C13 | Q16 | semidirect |
| 62. C3×C13 | C2×Q16 | semidirect |
| 84. C13 | D3×Q16 | semidirect |
| 104. D3 | #6107 | direct (N × H) |
| 112. C3 | C2×#6107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×C13 | 2 |
| D3×Dic26 | 2 |
| #10597670 | 2 |
| C3×#6107 | 2 |
| #10597606 | 2 |
| #10597604 | 2 |
| D3×#1055 | 2 |
| C2×#6107 | 3 |
| D3×Q16 | 13 |