Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. C2×C4×D39 | C2 | semidirect |
| 3. C3×C42×C13 | C2 | semidirect |
| 4. #10597666 | C2 | semidirect |
| 5. C4⋊Dic39 | C2 | semidirect |
| 12. D156 | C4 | direct (N × H) |
| 16. C42×C13 | D3 | semidirect |
| 22. C2×D39 | C2×C4 | semidirect |
| 24. C3×C4×C13 | C2×C4 | semidirect |
| 25. C3×C4×C13 | D4 | semidirect |
| 44. C4×C13 | C4×D3 | semidirect |
| 45. C4×C13 | D12 | semidirect |
| 49. C3×C42 | D13 | semidirect |
| 52. C3×C13 | C4×D4 | semidirect |
| 69. C42 | D39 | semidirect |
| 70. C13 | C4×D12 | semidirect |
| 76. C3×C4 | C4×D13 | semidirect |
| 77. C3×C4 | D52 | semidirect |
| 96. C4 | C4×D39 | semidirect |
| 97. C4 | D156 | direct (N × H) |
| 98. C3 | C4×D52 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D156 | 2 |
| C2×C4×D39 | 2 |
| C3×C42×C13 | 2 |
| #10597666 | 2 |
| C4⋊Dic39 | 2 |
| C4×D52 | 3 |
| C4×D12 | 13 |