Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16810439 | C2 | semidirect |
| 5. #20272818 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#1979 | C2 | semidirect |
| 12. C2×#13133163 | C4 | semidirect |
| 13. C2×#13133160 | C4 | semidirect |
| 165. #1979 | D53 | semidirect |
| 192. C53 | #13035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20283633 | 2 |
| C2×#16810439 | 2 |
| #20276442 | 2 |
| #20272818 | 2 |
| #20272801 | 2 |
| C53×#1979 | 2 |
| #13035 | 53 |