Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20273504 | C2 | semidirect |
| 4. #20273453 | C2 | semidirect |
| 6. #20272605 | C2 | semidirect |
| 7. C53×#1485 | C2 | semidirect |
| 165. #1485 | D53 | semidirect |
| 191. C53 | #10492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285653 | 2 |
| #20275555 | 2 |
| #20273504 | 2 |
| #20273453 | 2 |
| #20273382 | 2 |
| #20272605 | 2 |
| C53×#1485 | 2 |
| #10492 | 53 |