Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
152 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 152 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×D4×D13 | C2 | semidirect |
| 2. D12×D13 | C2 | semidirect |
| 3. #10597667 | C2 | semidirect |
| 4. C13×#213 | C2 | semidirect |
| 5. #10597596 | C2 | semidirect |
| 6. #10597595 | C2 | semidirect |
| 7. C3⋊C8×D13 | C2 | semidirect |
| 11. C3×D4×C13 | C22 | semidirect |
| 12. D156 | C22 | semidirect |
| 13. C13×D12 | C22 | semidirect |
| 15. C3×D52 | C22 | semidirect |
| 18. C3⋊#1055 | C22 | semidirect |
| 19. C13×C3⋊C8 | C22 | semidirect |
| 21. D4×D13 | D3 | semidirect |
| 39. D4×C13 | C2×D3 | semidirect |
| 43. D52 | C2×D3 | semidirect |
| 52. C3×D13 | D8 | semidirect |
| 68. #213 | D13 | direct (N × H) |
| 70. C3×C13 | C2×D8 | semidirect |
| 77. D13 | #213 | direct (N × H) |
| 82. C3×D4 | C2×D13 | semidirect |
| 86. D12 | C2×D13 | semidirect |
| 88. C3⋊C8 | C2×D13 | semidirect |
| 96. C13 | C2×#213 | semidirect |
| 113. D4 | D3×D13 | semidirect |
| 132. C3 | D8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×D13 | 2 |
| D12×D13 | 2 |
| #10597667 | 2 |
| C13×#213 | 2 |
| #10597596 | 2 |
| #10597595 | 2 |
| C3⋊C8×D13 | 2 |
| D8×D13 | 3 |
| C2×#213 | 13 |