Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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. C2×C3×Dic26 | C2 | semidirect |
| 3. C3×C13×M16 | C2 | semidirect |
| 4. C3×Dic52 | C2 | semidirect |
| 5. C3×#6095 | C2 | semidirect |
| 6. #88163 | C3 | direct (N × H) |
| 17. C2×Dic26 | C2×C3 | semidirect |
| 18. C13×M16 | C2×C3 | semidirect |
| 19. Dic52 | C2×C3 | semidirect |
| 20. #6095 | C2×C3 | semidirect |
| 50. C3×M16 | D13 | semidirect |
| 51. C3×C13 | #137 | semidirect |
| 69. M16 | C3×D13 | semidirect |
| 70. C13 | C3×#137 | semidirect |
| 95. C3 | #88163 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6127 | 2 |
| C2×C3×Dic26 | 2 |
| C3×C13×M16 | 2 |
| C3×Dic52 | 2 |
| C3×#6095 | 2 |
| #88163 | 3 |
| C3×#137 | 13 |