Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20273406 | C2 | semidirect |
| 4. #20273171 | C2 | semidirect |
| 6. #20272589 | C2 | semidirect |
| 7. C53×#1566 | C2 | semidirect |
| 178. #1566 | D53 | semidirect |
| 210. C53 | #10460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284514 | 2 |
| #20274704 | 2 |
| #20273406 | 2 |
| #20273171 | 2 |
| C2×#16810352 | 2 |
| #20272589 | 2 |
| C53×#1566 | 2 |
| #10460 | 53 |