Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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. C13×#208 | C2 | semidirect |
| 3. C3×#6099 | C2 | semidirect |
| 4. #10597594 | C2 | semidirect |
| 5. #10597591 | C2 | semidirect |
| 14. C3×#1055 | C22 | semidirect |
| 15. C13×C3⋊C8 | C22 | semidirect |
| 18. #6099 | D3 | semidirect |
| 37. #1055 | C2×D3 | semidirect |
| 42. D39 | M16 | semidirect |
| 53. #208 | D13 | semidirect |
| 56. C3×C13 | C2×M16 | semidirect |
| 70. C3⋊C8 | C2×D13 | semidirect |
| 76. C13 | D3×M16 | semidirect |
| 106. C3 | M16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D39 | 2 |
| C13×#208 | 2 |
| C3×#6099 | 2 |
| #10597594 | 2 |
| #10597591 | 2 |
| M16×D13 | 3 |
| D3×M16 | 13 |