Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C13×M16 | C2 | semidirect |
| 3. C13×#208 | C2 | semidirect |
| 4. C13×ΓL(1,𝔽25) | C2 | semidirect |
| 5. D3×C8×C13 | C2 | semidirect |
| 14. C3×C8×C13 | C22 | semidirect |
| 15. C13×C3⋊C8 | C22 | semidirect |
| 19. C13×M16 | D3 | direct (N × H) |
| 37. C8×C13 | C2×D3 | semidirect |
| 38. D3×M16 | C13 | direct (N × H) |
| 42. D3×C13 | M16 | direct (N × H) |
| 52. C3×M16 | C2×C13 | semidirect |
| 53. #208 | C2×C13 | semidirect |
| 54. ΓL(1,𝔽25) | C2×C13 | semidirect |
| 55. D3×C8 | C2×C13 | semidirect |
| 56. C3×C13 | C2×M16 | semidirect |
| 69. C3×C8 | C22×C13 | semidirect |
| 70. C3⋊C8 | C22×C13 | semidirect |
| 74. M16 | D3×C13 | direct (N × H) |
| 76. C13 | D3×M16 | direct (N × H) |
| 93. C8 | C2×D3×C13 | semidirect |
| 97. D3 | C13×M16 | direct (N × H) |
| 106. C3 | C2×C13×M16 | 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 |
| C3×C13×M16 | 2 |
| C13×#208 | 2 |
| C13×ΓL(1,𝔽25) | 2 |
| D3×C8×C13 | 2 |
| C2×C13×M16 | 3 |
| D3×M16 | 13 |