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×C3×Dic13 | C2 | semidirect |
| 3. C3×C22⋊Dic13 | C2 | semidirect |
| 4. C3×C4⋊Dic13 | C2 | semidirect |
| 5. C3×C4×Dic13 | C2 | semidirect |
| 6. D4×Dic13 | C3 | direct (N × H) |
| 8. C3×D4×C13 | C4 | semidirect |
| 15. C22×Dic13 | C2×C3 | semidirect |
| 16. C22⋊Dic13 | C2×C3 | semidirect |
| 17. C4⋊Dic13 | C2×C3 | semidirect |
| 18. C4×Dic13 | C2×C3 | semidirect |
| 21. C22×C3×C13 | C2×C4 | semidirect |
| 23. C3×C4×C13 | C2×C4 | semidirect |
| 26. C3×Dic13 | D4 | direct (N × H) |
| 28. D4×C13 | C3×C4 | semidirect |
| 41. C22×C13 | C2×C3×C4 | semidirect |
| 43. C4×C13 | C2×C3×C4 | semidirect |
| 46. Dic13 | C3×D4 | direct (N × H) |
| 52. C3×C13 | C4×D4 | semidirect |
| 59. C3×D4 | Dic13 | direct (N × H) |
| 70. C13 | C3×C4×D4 | semidirect |
| 73. C22×C3 | C2×Dic13 | semidirect |
| 78. C3×C4 | C2×Dic13 | semidirect |
| 80. D4 | C3×Dic13 | direct (N × H) |
| 92. C22 | C2×C3×Dic13 | semidirect |
| 97. C4 | C2×C3×Dic13 | semidirect |
| 98. C3 | D4×Dic13 | direct (N × H) |
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×C3×Dic13 | 2 |
| C3×C22⋊Dic13 | 2 |
| C3×C4⋊Dic13 | 2 |
| C3×C4×Dic13 | 2 |
| D4×Dic13 | 3 |
| C3×C4×D4 | 13 |