Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275490 | C2 | semidirect |
| 3. #20273490 | C2 | semidirect |
| 6. #20272590 | C2 | semidirect |
| 7. C53×#1565 | C2 | semidirect |
| 155. #1565 | D53 | semidirect |
| 182. C53 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275555 | 2 |
| #20275490 | 2 |
| #20273490 | 2 |
| #20273382 | 2 |
| C2×#16810366 | 2 |
| #20272590 | 2 |
| C53×#1565 | 2 |
| #10603 | 53 |