Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 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×#64625 | C2 | semidirect |
| 3. #10597790 | C2 | direct (N × H) |
| 4. C2×D156 | C2 | semidirect |
| 5. C2×C4×D39 | C2 | semidirect |
| 6. C2×Dic78 | C2 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 13. #64625 | C22 | semidirect |
| 15. D156 | C22 | semidirect |
| 16. C4×D39 | C22 | semidirect |
| 17. Dic78 | C22 | semidirect |
| 18. C22×C4×C13 | D3 | semidirect |
| 36. C2×C4×C13 | C2×D3 | semidirect |
| 44. C2×C3×C13 | #41 | semidirect |
| 55. C22×C3×C4 | D13 | semidirect |
| 61. C3×C13 | C2×#41 | semidirect |
| 64. C2×C13 | #235 | semidirect |
| 71. C2×C3×C4 | C2×D13 | semidirect |
| 82. C22×C4 | D39 | semidirect |
| 83. C13 | C2×#235 | semidirect |
| 101. C2×C4 | C2×D39 | semidirect |
| 103. C2×C3 | #6127 | semidirect |
| 114. C3 | C2×#6127 | semidirect |
| 117. C2 | #10597790 | 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×#64625 | 2 |
| #10597790 | 2 |
| C2×D156 | 2 |
| C2×C4×D39 | 2 |
| C2×Dic78 | 2 |
| C2×#6127 | 3 |
| C2×#235 | 13 |