Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 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 |
|---|---|---|
| 1. C3×#6127 | C2 | semidirect |
| 2. C2×C3×D52 | C2 | semidirect |
| 3. C3×C13×M16 | C2 | semidirect |
| 4. C3×D104 | C2 | semidirect |
| 5. C3×#6095 | C2 | semidirect |
| 6. #88162 | C3 | direct (N × H) |
| 12. C3×D52 | C22 | semidirect |
| 14. C3×Dic26 | C22 | semidirect |
| 15. C3×C8×C13 | C22 | semidirect |
| 16. #6127 | C2×C3 | semidirect |
| 17. C2×D52 | C2×C3 | semidirect |
| 18. C13×M16 | C2×C3 | semidirect |
| 19. D104 | C2×C3 | semidirect |
| 20. #6095 | C2×C3 | semidirect |
| 33. D52 | C22×C3 | semidirect |
| 35. Dic26 | C22×C3 | semidirect |
| 36. C8×C13 | C22×C3 | semidirect |
| 53. C3×M16 | D13 | semidirect |
| 54. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 68. C3×C8 | C2×D13 | semidirect |
| 73. M16 | C3×D13 | semidirect |
| 74. C13 | C3×AGL(1,ℤ/8) | semidirect |
| 90. C8 | C2×C3×D13 | semidirect |
| 102. C3 | #88162 | 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×D52 | 2 |
| C3×C13×M16 | 2 |
| C3×D104 | 2 |
| C3×#6095 | 2 |
| #88162 | 3 |
| C3×AGL(1,ℤ/8) | 13 |