Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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×Q8×D13 | C2 | semidirect |
| 3. #10597669 | C2 | semidirect |
| 4. C13×#215 | C2 | semidirect |
| 5. #10597601 | C2 | semidirect |
| 6. #10597599 | C2 | semidirect |
| 7. C3⋊C8×D13 | C2 | semidirect |
| 10. C3×Q8×C13 | C22 | semidirect |
| 16. C3×Dic26 | C22 | semidirect |
| 18. C3⋊#1055 | C22 | semidirect |
| 19. C13×C3⋊C8 | C22 | semidirect |
| 20. Q8×D13 | D3 | semidirect |
| 36. Q8×C13 | C2×D3 | semidirect |
| 43. Dic26 | C2×D3 | semidirect |
| 49. C3×D13 | SD16 | semidirect |
| 64. #215 | D13 | direct (N × H) |
| 66. C3×C13 | C2×SD16 | semidirect |
| 71. D13 | #215 | direct (N × H) |
| 75. C3×Q8 | C2×D13 | semidirect |
| 82. C3⋊C8 | C2×D13 | semidirect |
| 90. C13 | C2×#215 | semidirect |
| 102. Q8 | D3×D13 | semidirect |
| 122. C3 | SD16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D13 | 2 |
| D12×D13 | 2 |
| #10597669 | 2 |
| C13×#215 | 2 |
| #10597601 | 2 |
| #10597599 | 2 |
| C3⋊C8×D13 | 2 |
| SD16×D13 | 3 |
| C2×#215 | 13 |