Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
848 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 208 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 |
|---|---|---|
| 1. #20291611 | C2 | semidirect |
| 3. #20289987 | C2 | semidirect |
| 4. #20289978 | C2 | semidirect |
| 187. C53 | #17410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291611 | 2 |
| #20289999 | 2 |
| #20289987 | 2 |
| #20289978 | 2 |
| #20289968 | 2 |
| C2×#16811234 | 2 |
| #17410 | 53 |