Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
834 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #20289210 | C2 | semidirect |
| 3. #20273870 | C2 | semidirect |
| 4. #20273808 | C2 | semidirect |
| 5. #20273453 | C2 | semidirect |
| 6. #20273171 | C2 | semidirect |
| 185. C53 | #18698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289210 | 2 |
| #20286102 | 2 |
| #20273870 | 2 |
| #20273808 | 2 |
| #20273453 | 2 |
| #20273171 | 2 |
| C53×#3131 | 2 |
| #18698 | 53 |