Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16810731 | C2 | semidirect |
| 3. C2×#16810438 | C2 | semidirect |
| 5. #20272815 | C2 | semidirect |
| 6. #20272795 | C2 | semidirect |
| 12. C2×#13133163 | C4 | semidirect |
| 13. C2×#13133161 | C4 | semidirect |
| 196. C53 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811063 | 2 |
| C2×#16810731 | 2 |
| C2×#16810438 | 2 |
| C2×#16810433 | 2 |
| #20272815 | 2 |
| #20272795 | 2 |
| C53×#1975 | 2 |
| #13038 | 53 |