Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20285917 | C2 | semidirect |
| 5. #20273070 | C2 | semidirect |
| 6. #20272587 | C2 | semidirect |
| 7. C53×#1485 | C2 | semidirect |
| 178. #1485 | D53 | semidirect |
| 211. C53 | #10123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285917 | 2 |
| #20285913 | 2 |
| #20285116 | 2 |
| #20273185 | 2 |
| #20273070 | 2 |
| #20272587 | 2 |
| C53×#1485 | 2 |
| #10123 | 53 |