Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20285907 | C2 | semidirect |
| 3. #20279876 | C2 | semidirect |
| 4. #20275633 | C2 | semidirect |
| 5. #20273318 | C2 | semidirect |
| 6. #20273157 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 216. #1285 | D53 | semidirect |
| 249. C53 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285907 | 2 |
| #20284807 | 2 |
| #20279876 | 2 |
| #20275633 | 2 |
| #20273318 | 2 |
| #20273157 | 2 |
| C53×#1285 | 2 |
| #10005 | 53 |