Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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. C13×#235 | C2 | direct (N × H) |
| 4. C2×C13×D12 | C2 | semidirect |
| 5. C2×C4×D3×C13 | C2 | semidirect |
| 6. C2×C13×Dic6 | C2 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 13. C13×#67 | C22 | semidirect |
| 15. C13×D12 | C22 | semidirect |
| 16. C4×D3×C13 | C22 | semidirect |
| 17. C13×Dic6 | C22 | semidirect |
| 23. C22×C4×C13 | D3 | semidirect |
| 41. C2×C4×C13 | C2×D3 | semidirect |
| 42. C2×#235 | C13 | direct (N × H) |
| 44. C2×C3×C13 | #41 | semidirect |
| 55. C22×C3×C4 | C2×C13 | semidirect |
| 56. C2×#67 | C2×C13 | semidirect |
| 57. #235 | C2×C13 | direct (N × H) |
| 58. C2×D12 | C2×C13 | semidirect |
| 59. C2×C4×D3 | C2×C13 | semidirect |
| 60. C2×Dic6 | C2×C13 | semidirect |
| 61. C3×C13 | C2×#41 | semidirect |
| 65. C2×C13 | #235 | direct (N × H) |
| 71. C2×C3×C4 | C22×C13 | semidirect |
| 72. #67 | C22×C13 | semidirect |
| 74. D12 | C22×C13 | semidirect |
| 75. C4×D3 | C22×C13 | semidirect |
| 76. Dic6 | C22×C13 | semidirect |
| 82. C22×C4 | D3×C13 | semidirect |
| 83. C13 | C2×#235 | direct (N × H) |
| 101. C2×C4 | C2×D3×C13 | semidirect |
| 103. C2×C3 | C13×#41 | semidirect |
| 114. C3 | C2×C13×#41 | semidirect |
| 117. C2 | C13×#235 | direct (N × H) |
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 |
| C13×#235 | 2 |
| C2×C13×D12 | 2 |
| C2×C4×D3×C13 | 2 |
| C2×C13×Dic6 | 2 |
| C2×C13×#41 | 3 |
| C2×#235 | 13 |