Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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×#6131 | C2 | semidirect |
| 2. D12×D13 | C2 | semidirect |
| 3. #10597669 | C2 | semidirect |
| 4. C13×#215 | C2 | semidirect |
| 5. #10597596 | C2 | semidirect |
| 6. #10597595 | C2 | semidirect |
| 7. #10597592 | C2 | semidirect |
| 10. C3×Q8×C13 | C22 | semidirect |
| 14. C3×D52 | C22 | semidirect |
| 18. C3⋊#1055 | C22 | semidirect |
| 19. C13×C3⋊C8 | C22 | semidirect |
| 20. #6131 | D3 | semidirect |
| 36. Q8×C13 | C2×D3 | semidirect |
| 41. D52 | C2×D3 | semidirect |
| 63. #215 | D13 | semidirect |
| 67. C3×C13 | AGL(1,ℤ/8) | semidirect |
| 75. C3×Q8 | C2×D13 | semidirect |
| 84. C3⋊C8 | C2×D13 | semidirect |
| 92. C13 | #949 | semidirect |
| 102. Q8 | D3×D13 | semidirect |
| 125. C3 | #88168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6131 | 2 |
| D12×D13 | 2 |
| #10597669 | 2 |
| C13×#215 | 2 |
| #10597596 | 2 |
| #10597595 | 2 |
| #10597592 | 2 |
| #88168 | 3 |
| #949 | 13 |