Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 4. #20273266 | C2 | semidirect |
| 5. #20272580 | C2 | semidirect |
| 6. #20272577 | C2 | semidirect |
| 7. C53×#1485 | C2 | semidirect |
| 9. #16811029 | C4 | semidirect |
| 10. #16811029 | C4 | semidirect |
| 11. #16810985 | C4 | semidirect |
| 12. #16810985 | C4 | semidirect |
| 189. #1485 | D53 | semidirect |
| 224. C53 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285955 | 2 |
| #20283700 | 2 |
| #20273293 | 2 |
| #20273266 | 2 |
| #20272580 | 2 |
| #20272577 | 2 |
| C53×#1485 | 2 |
| #9369 | 53 |