Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. #16810919 | C4 | semidirect |
| 13. #16810909 | C4 | semidirect |
| 211. C53 | #9176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284522 | 2 |
| #20277632 | 2 |
| #20273278 | 2 |
| #20273215 | 2 |
| #20273109 | 2 |
| #20272616 | 2 |
| C53×#1286 | 2 |
| #9176 | 53 |