Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20289978 | C2 | semidirect |
| 4. #20289566 | C2 | semidirect |
| 221. C53 | #9458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291611 | 2 |
| #20290242 | 2 |
| #20289978 | 2 |
| #20289566 | 2 |
| #20279715 | 2 |
| #9458 | 53 |