Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 74 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. C22×C3×C4×C13 | C2 | semidirect |
| 2. C2×C13×#67 | C2 | semidirect |
| 3. C2×C13×D12 | C2 | semidirect |
| 4. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C13×C4⋊Dic3 | C2 | semidirect |
| 17. C22×C4×C13 | D3 | semidirect |
| 22. C22×C3×C13 | D4 | semidirect |
| 28. C3×C4×C13 | D4 | semidirect |
| 38. #930 | C13 | direct (N × H) |
| 49. C22×C13 | D12 | semidirect |
| 53. C4×C13 | #67 | semidirect |
| 54. C22×C3×C4 | C2×C13 | semidirect |
| 55. C2×#67 | C2×C13 | semidirect |
| 56. C2×D12 | C2×C13 | semidirect |
| 57. (C2×D3)⋊C4 | C2×C13 | semidirect |
| 58. C4⋊Dic3 | C2×C13 | semidirect |
| 59. C3×C13 | #121 | semidirect |
| 76. C22×C4 | D3×C13 | semidirect |
| 79. C13 | #930 | direct (N × H) |
| 82. C22×C3 | D4×C13 | semidirect |
| 88. C3×C4 | D4×C13 | semidirect |
| 108. C22 | C13×D12 | semidirect |
| 112. C4 | C13×#67 | semidirect |
| 113. C3 | C13×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C13 | 2 |
| C2×C13×#67 | 2 |
| C2×C13×D12 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×C4⋊Dic3 | 2 |
| C13×#121 | 3 |
| #930 | 13 |