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. D3×Q8×C13 | C2 | semidirect |
| 3. #10597669 | C2 | semidirect |
| 4. C3×#6106 | C2 | semidirect |
| 5. #10597603 | C2 | semidirect |
| 6. #10597598 | C2 | semidirect |
| 7. D3×#1055 | C2 | semidirect |
| 10. C3×Q8×C13 | C22 | semidirect |
| 15. C13×Dic6 | C22 | semidirect |
| 18. C3⋊#1055 | C22 | semidirect |
| 19. C3×#1055 | C22 | semidirect |
| 25. #6106 | D3 | direct (N × H) |
| 38. Q8×C13 | C2×D3 | semidirect |
| 45. #1055 | C2×D3 | semidirect |
| 50. D3×C13 | SD16 | semidirect |
| 59. D3×Q8 | D13 | semidirect |
| 66. C3×C13 | C2×SD16 | semidirect |
| 73. C3×Q8 | C2×D13 | semidirect |
| 80. Dic6 | C2×D13 | semidirect |
| 90. C13 | D3×SD16 | semidirect |
| 102. Q8 | D3×D13 | semidirect |
| 113. D3 | #6106 | direct (N × H) |
| 122. C3 | C2×#6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×C13 | 2 |
| D3×D52 | 2 |
| #10597669 | 2 |
| C3×#6106 | 2 |
| #10597603 | 2 |
| #10597598 | 2 |
| D3×#1055 | 2 |
| C2×#6106 | 3 |
| D3×SD16 | 13 |