Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C3×Dic26 | C2 | semidirect |
| 5. C3×C4⋊Dic13 | C2 | semidirect |
| 6. C3×#6101 | C2 | semidirect |
| 7. C3×#6101 | C2 | semidirect |
| 8. #88132 | C3 | direct (N × H) |
| 19. C2×Dic26 | C2×C3 | semidirect |
| 22. C4⋊Dic13 | C2×C3 | semidirect |
| 23. #6101 | C2×C3 | semidirect |
| 24. #6101 | C2×C3 | semidirect |
| 27. C22×C3×C13 | Q8 | semidirect |
| 51. C22×C13 | C3×Q8 | semidirect |
| 66. C3×C13 | C22⋊Q8 | semidirect |
| 88. C13 | C3×C22⋊Q8 | semidirect |
| 91. C22×C3 | Dic26 | semidirect |
| 114. C22 | C3×Dic26 | semidirect |
| 122. C3 | #88132 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic13 | 2 |
| C2×C3×Dic26 | 2 |
| C3×C13×C22⋊C4 | 2 |
| C3×C22⋊Dic13 | 2 |
| C3×C4⋊Dic13 | 2 |
| C3×#6101 | 2 |
| #88132 | 3 |
| C3×C22⋊Q8 | 13 |