Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
124 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 124 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. #10597790 | C2 | semidirect |
| 2. C13×#235 | C2 | semidirect |
| 3. C2×C3×#1055 | C2 | semidirect |
| 4. #10597606 | C2 | semidirect |
| 5. #10597603 | C2 | semidirect |
| 6. #10597602 | C2 | semidirect |
| 7. #10597597 | C2 | semidirect |
| 26. C2×#1055 | D3 | semidirect |
| 58. #235 | D13 | semidirect |
| 64. C3×C13 | #135 | semidirect |
| 88. C13 | #904 | semidirect |
| 118. C3 | #88204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597790 | 2 |
| C13×#235 | 2 |
| C2×C3×#1055 | 2 |
| #10597606 | 2 |
| #10597603 | 2 |
| #10597602 | 2 |
| #10597597 | 2 |
| #88204 | 3 |
| #904 | 13 |