Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20283810 | C2 | semidirect |
| 5. #20272626 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 7. C53×#1559 | C2 | semidirect |
| 166. #1559 | D53 | semidirect |
| 197. C53 | #9530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20283810 | 2 |
| #20273139 | 2 |
| #20273055 | 2 |
| #20272626 | 2 |
| #20272576 | 2 |
| C53×#1559 | 2 |
| #9530 | 53 |