Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10597662 | C2 | semidirect |
| 3. C3×#6099 | C2 | semidirect |
| 4. #10597593 | C2 | semidirect |
| 5. D3×#1055 | C2 | semidirect |
| 14. C3⋊#1055 | C22 | semidirect |
| 15. C3×#1055 | C22 | semidirect |
| 19. #6099 | D3 | direct (N × H) |
| 37. #1055 | C2×D3 | semidirect |
| 42. D3×C13 | M16 | semidirect |
| 56. C3×C13 | C2×M16 | semidirect |
| 76. C13 | D3×M16 | semidirect |
| 97. D3 | #6099 | direct (N × H) |
| 106. C3 | C2×#6099 | 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 |
| #10597662 | 2 |
| C3×#6099 | 2 |
| #10597593 | 2 |
| D3×#1055 | 2 |
| C2×#6099 | 3 |
| D3×M16 | 13 |