Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 57 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×Dic78 | C2 | semidirect |
| 5. C4⋊Dic39 | C2 | semidirect |
| 6. #10597664 | C2 | semidirect |
| 7. #10597664 | C2 | semidirect |
| 27. C22×C3×C13 | Q8 | semidirect |
| 51. C22×C13 | Dic6 | semidirect |
| 66. C3×C13 | C22⋊Q8 | semidirect |
| 88. C13 | #878 | semidirect |
| 91. C22×C3 | Dic26 | semidirect |
| 114. C22 | Dic78 | semidirect |
| 122. C3 | #88132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic39 | 2 |
| C2×Dic78 | 2 |
| C3×C13×C22⋊C4 | 2 |
| #10597671 | 2 |
| C4⋊Dic39 | 2 |
| #10597664 | 2 |
| #88132 | 3 |
| #878 | 13 |