Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
264 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×C3×C4×C13 | C2 | semidirect |
| 3. C22×Dic3×C13 | C2 | semidirect |
| 4. C13×(C2×D3)⋊C4 | C2 | direct (N × H) |
| 9. C22×D3×C13 | C4 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 14. C2×Dic3×C13 | C22 | semidirect |
| 17. C22×C4×C13 | D3 | semidirect |
| 26. C2×D3×C13 | C2×C4 | semidirect |
| 37. C2×C4×C13 | C2×D3 | semidirect |
| 38. C2×(C2×D3)⋊C4 | C13 | direct (N × H) |
| 39. C2×C3×C13 | C22⋊C4 | semidirect |
| 55. C22×C3×C4 | C2×C13 | semidirect |
| 56. C22×Dic3 | C2×C13 | semidirect |
| 57. (C2×D3)⋊C4 | C2×C13 | direct (N × H) |
| 58. C3×C13 | C2×C22⋊C4 | semidirect |
| 61. C2×C13 | (C2×D3)⋊C4 | direct (N × H) |
| 68. C22×D3 | C4×C13 | semidirect |
| 71. C2×C3×C4 | C22×C13 | semidirect |
| 73. C2×Dic3 | C22×C13 | semidirect |
| 76. C22×C4 | D3×C13 | semidirect |
| 78. C13 | C2×(C2×D3)⋊C4 | direct (N × H) |
| 86. C2×D3 | C2×C4×C13 | semidirect |
| 97. C2×C4 | C2×D3×C13 | semidirect |
| 98. C2×C3 | C13×C22⋊C4 | semidirect |
| 113. C3 | C2×C13×C22⋊C4 | semidirect |
| 115. C2 | C13×(C2×D3)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D3×C13 | 2 |
| C22×C3×C4×C13 | 2 |
| C22×Dic3×C13 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C2×C13×C22⋊C4 | 3 |
| C2×(C2×D3)⋊C4 | 13 |