Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 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. C23×D3×C13 | C2 | semidirect |
| 2. C2×C13×#67 | C2 | semidirect |
| 3. C2×C13×D12 | C2 | semidirect |
| 4. C3×C13×C22⋊C4 | C2 | semidirect |
| 5. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 11. C22×D3×C13 | C22 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 14. C2×Dic3×C13 | C22 | semidirect |
| 20. C13×C22⋊C4 | D3 | semidirect |
| 22. C22×C3×C13 | D4 | semidirect |
| 29. C2×D3×C13 | D4 | semidirect |
| 40. C2×C4×C13 | C2×D3 | semidirect |
| 41. #882 | C13 | direct (N × H) |
| 54. C22×C13 | D12 | semidirect |
| 58. C23×D3 | C2×C13 | semidirect |
| 59. C2×#67 | C2×C13 | semidirect |
| 60. C2×D12 | C2×C13 | semidirect |
| 61. C3×C22⋊C4 | C2×C13 | semidirect |
| 62. (C2×D3)⋊C4 | C2×C13 | semidirect |
| 63. C3×C13 | #120 | semidirect |
| 74. C22×D3 | C22×C13 | semidirect |
| 75. C2×C3×C4 | C22×C13 | semidirect |
| 77. C2×Dic3 | C22×C13 | semidirect |
| 83. C22⋊C4 | D3×C13 | semidirect |
| 84. C13 | #882 | direct (N × H) |
| 86. C22×C3 | D4×C13 | semidirect |
| 93. C2×D3 | D4×C13 | semidirect |
| 104. C2×C4 | C2×D3×C13 | semidirect |
| 117. C22 | C13×D12 | semidirect |
| 121. C3 | C13×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D3×C13 | 2 |
| C2×C13×#67 | 2 |
| C2×C13×D12 | 2 |
| C3×C13×C22⋊C4 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×#120 | 3 |
| #882 | 13 |