Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #20283809 | C2 | semidirect |
| 3. #20273329 | C2 | semidirect |
| 6. #20272577 | C2 | semidirect |
| 7. C53×#1275 | C2 | semidirect |
| 164. #1275 | D53 | semidirect |
| 191. C53 | #9284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285853 | 2 |
| #20283809 | 2 |
| #20273329 | 2 |
| #20273325 | 2 |
| #20273185 | 2 |
| #20272577 | 2 |
| C53×#1275 | 2 |
| #9284 | 53 |