Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C13×#67 | C2 | semidirect |
| 2. C2×C13×#67 | C2 | semidirect |
| 3. C2×C13×D12 | C2 | semidirect |
| 4. C2×C4×D3×C13 | C2 | semidirect |
| 5. C3×C13×C22⋊C4 | C2 | semidirect |
| 6. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C13×Dic3⋊C4 | C2 | semidirect |
| 26. C13×C22⋊C4 | D3 | semidirect |
| 36. C2×D3×C13 | D4 | semidirect |
| 40. Dic3×C13 | D4 | semidirect |
| 52. #884 | C13 | direct (N × H) |
| 73. C2×#67 | C2×C13 | semidirect |
| 74. C2×#67 | C2×C13 | semidirect |
| 75. C2×D12 | C2×C13 | semidirect |
| 76. C2×C4×D3 | C2×C13 | semidirect |
| 77. C3×C22⋊C4 | C2×C13 | semidirect |
| 78. (C2×D3)⋊C4 | C2×C13 | semidirect |
| 79. Dic3⋊C4 | C2×C13 | semidirect |
| 80. C3×C13 | #121 | semidirect |
| 105. C22⋊C4 | D3×C13 | semidirect |
| 106. C13 | #884 | direct (N × H) |
| 116. C2×D3 | D4×C13 | semidirect |
| 120. Dic3 | D4×C13 | semidirect |
| 152. C3 | C13×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#67 | 2 |
| C2×C13×D12 | 2 |
| C2×C4×D3×C13 | 2 |
| C3×C13×C22⋊C4 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×Dic3⋊C4 | 2 |
| C13×#121 | 3 |
| #884 | 13 |