Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 102 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×Dic3×C13 | C2 | semidirect |
| 3. C13×#217 | C2 | semidirect |
| 4. C13×C4⋊Dic3 | C2 | semidirect |
| 5. C4×Dic3×C13 | C2 | semidirect |
| 8. C3×D4×C13 | C4 | semidirect |
| 21. C22×C3×C13 | C2×C4 | semidirect |
| 23. C3×C4×C13 | C2×C4 | semidirect |
| 26. Dic3×C13 | D4 | direct (N × H) |
| 28. D4×C13 | Dic3 | direct (N × H) |
| 34. D4×Dic3 | C13 | direct (N × H) |
| 41. C22×C13 | C2×Dic3 | semidirect |
| 46. C4×C13 | C2×Dic3 | semidirect |
| 48. C22×Dic3 | C2×C13 | semidirect |
| 49. #217 | C2×C13 | semidirect |
| 50. C4⋊Dic3 | C2×C13 | semidirect |
| 51. C4×Dic3 | C2×C13 | semidirect |
| 52. C3×C13 | C4×D4 | semidirect |
| 59. C3×D4 | C4×C13 | semidirect |
| 70. C13 | D4×Dic3 | direct (N × H) |
| 73. C22×C3 | C2×C4×C13 | semidirect |
| 75. C3×C4 | C2×C4×C13 | semidirect |
| 78. Dic3 | D4×C13 | direct (N × H) |
| 80. D4 | Dic3×C13 | direct (N × H) |
| 92. C22 | C2×Dic3×C13 | semidirect |
| 97. C4 | C2×Dic3×C13 | semidirect |
| 98. C3 | C4×D4×C13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C13 | 2 |
| C22×Dic3×C13 | 2 |
| C13×#217 | 2 |
| C13×C4⋊Dic3 | 2 |
| C4×Dic3×C13 | 2 |
| C4×D4×C13 | 3 |
| D4×Dic3 | 13 |