Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
184 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C3×C13×C4⋊C4 | C2 | semidirect |
| 4. C3×C4⋊Dic13 | C2 | semidirect |
| 5. C3×#6101 | C2 | semidirect |
| 6. C4⋊C4×D13 | C3 | direct (N × H) |
| 13. C3×C4×D13 | C4 | semidirect |
| 16. C13×C4⋊C4 | C2×C3 | semidirect |
| 17. C4⋊Dic13 | C2×C3 | semidirect |
| 18. #6101 | C2×C3 | semidirect |
| 24. C3×C4×C13 | C2×C4 | semidirect |
| 26. C3×Dic13 | C2×C4 | semidirect |
| 33. C4×D13 | C3×C4 | semidirect |
| 38. C3×D13 | C4⋊C4 | direct (N × H) |
| 44. C4×C13 | C2×C3×C4 | semidirect |
| 46. Dic13 | C2×C3×C4 | semidirect |
| 51. C3×C4⋊C4 | D13 | direct (N × H) |
| 52. C3×C13 | C2×C4⋊C4 | semidirect |
| 57. D13 | C3×C4⋊C4 | direct (N × H) |
| 69. C4⋊C4 | C3×D13 | direct (N × H) |
| 70. C13 | C2×C3×C4⋊C4 | semidirect |
| 78. C3×C4 | C4×D13 | semidirect |
| 97. C4 | C3×C4×D13 | semidirect |
| 98. C3 | C4⋊C4×D13 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D13 | 2 |
| C3×C13×C4⋊C4 | 2 |
| C3×C4⋊Dic13 | 2 |
| C3×#6101 | 2 |
| C4⋊C4×D13 | 3 |
| C2×C3×C4⋊C4 | 13 |