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. Q8×D39 | C2 | semidirect |
| 3. C13×#215 | C2 | semidirect |
| 4. C3×#6106 | C2 | semidirect |
| 5. #10597602 | C2 | semidirect |
| 6. #10597600 | C2 | semidirect |
| 7. #10597591 | C2 | semidirect |
| 10. C3×Q8×C13 | C22 | semidirect |
| 14. Dic78 | C22 | semidirect |
| 18. C3×#1055 | C22 | semidirect |
| 19. C13×C3⋊C8 | C22 | semidirect |
| 23. #6106 | D3 | semidirect |
| 36. Q8×C13 | C2×D3 | semidirect |
| 45. #1055 | C2×D3 | semidirect |
| 48. D39 | SD16 | semidirect |
| 62. #215 | D13 | semidirect |
| 66. C3×C13 | C2×SD16 | semidirect |
| 73. C3×Q8 | C2×D13 | semidirect |
| 82. C3⋊C8 | C2×D13 | semidirect |
| 90. C13 | D3×SD16 | 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 |
|---|---|
| Q8×D39 | 2 |
| #10597743 | 2 |
| C13×#215 | 2 |
| C3×#6106 | 2 |
| #10597602 | 2 |
| #10597600 | 2 |
| #10597591 | 2 |
| SD16×D13 | 3 |
| D3×SD16 | 13 |