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. #20273265 | C2 | semidirect |
| 5. #20273137 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 7. C53×#1288 | C2 | semidirect |
| 10. #16811032 | C4 | semidirect |
| 11. #16811032 | C4 | semidirect |
| 12. #16810983 | C4 | semidirect |
| 13. #16810983 | C4 | semidirect |
| 190. #1288 | 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 |
|---|---|
| #20285957 | 2 |
| #20283700 | 2 |
| #20273290 | 2 |
| #20273265 | 2 |
| #20273137 | 2 |
| #20272576 | 2 |
| C53×#1288 | 2 |
| #9369 | 53 |