Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. #20283695 | C2 | semidirect |
| 3. #20273290 | C2 | semidirect |
| 4. #20273132 | C2 | semidirect |
| 5. #20272579 | C2 | semidirect |
| 6. #20272578 | C2 | semidirect |
| 7. C53×#1514 | C2 | semidirect |
| 9. #16811015 | C4 | semidirect |
| 10. #16811010 | C4 | semidirect |
| 11. #16810991 | C4 | semidirect |
| 12. #16810987 | C4 | semidirect |
| 202. #1514 | D53 | semidirect |
| 239. C53 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285752 | 2 |
| #20283695 | 2 |
| #20273290 | 2 |
| #20273132 | 2 |
| #20272579 | 2 |
| #20272578 | 2 |
| C53×#1514 | 2 |
| #9370 | 53 |