Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
570 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20273288 | C2 | semidirect |
| 4. #20272595 | C2 | semidirect |
| 8. #16810562 | C4 | semidirect |
| 9. #16810559 | C4 | semidirect |
| 10. #16810543 | C4 | semidirect |
| 11. #16810535 | C4 | semidirect |
| 218. C53 | #9383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279891 | 2 |
| #20274703 | 2 |
| #20273288 | 2 |
| #20272595 | 2 |
| C53×#2972 | 2 |
| #9383 | 53 |