Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 8. C22×#11719925 | C4 | semidirect |
| 16. #16810659 | C4 | semidirect |
| 17. #16810632 | C4 | semidirect |
| 18. #16810631 | C4 | semidirect |
| 234. C53 | #13233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284367 | 2 |
| #20276409 | 2 |
| #20276370 | 2 |
| #20276369 | 2 |
| #20274763 | 2 |
| #20274518 | 2 |
| C53×#2135 | 2 |
| #13233 | 53 |