Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20273331 | C2 | semidirect |
| 4. #20273280 | C2 | semidirect |
| 6. #20272597 | C2 | semidirect |
| 7. C53×#1302 | C2 | semidirect |
| 10. #16811032 | C4 | semidirect |
| 11. #16811017 | C4 | semidirect |
| 12. #16810992 | C4 | semidirect |
| 13. #16810983 | C4 | semidirect |
| 198. #1302 | D53 | semidirect |
| 233. C53 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285424 | 2 |
| #20283704 | 2 |
| #20273331 | 2 |
| #20273280 | 2 |
| #20273254 | 2 |
| #20272597 | 2 |
| C53×#1302 | 2 |
| #9431 | 53 |