Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 4. C3×C4⋊Dic13 | C2 | semidirect |
| 5. C3×#6101 | C2 | semidirect |
| 6. C3×#6101 | C2 | semidirect |
| 7. C3×C4×Dic13 | C2 | semidirect |
| 8. #88133 | C3 | direct (N × H) |
| 19. C4⋊Dic13 | C2×C3 | semidirect |
| 20. #6101 | C2×C3 | semidirect |
| 21. #6101 | C2×C3 | semidirect |
| 22. C4×Dic13 | C2×C3 | semidirect |
| 62. C3×C13 | #126 | semidirect |
| 82. C13 | C3×#126 | semidirect |
| 114. C3 | #88133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C13×C22⋊C4 | 2 |
| C3×C22⋊Dic13 | 2 |
| C3×C4⋊Dic13 | 2 |
| C3×#6101 | 2 |
| C3×C4×Dic13 | 2 |
| #88133 | 3 |
| C3×#126 | 13 |