Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20274852 | C2 | semidirect |
| 3. #20273384 | C2 | semidirect |
| 4. #20273383 | C2 | semidirect |
| 5. #20273382 | C2 | semidirect |
| 6. #20273008 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 166. #1545 | D53 | semidirect |
| 192. C53 | #9780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810999 | 2 |
| #20274852 | 2 |
| #20273384 | 2 |
| #20273383 | 2 |
| #20273382 | 2 |
| #20273008 | 2 |
| C53×#1545 | 2 |
| #9780 | 53 |