Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
546 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 157 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. #20272585 | C2 | semidirect |
| 4. #20272584 | C2 | semidirect |
| 5. C53×#1290 | C2 | semidirect |
| 138. #1290 | D53 | semidirect |
| 159. C53 | #7986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #432×D53 | 2 |
| C2×#16810675 | 2 |
| #20272585 | 2 |
| #20272584 | 2 |
| C53×#1290 | 2 |
| #7986 | 53 |