Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 430 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. C2×#16810438 | C2 | semidirect |
| 5. C2×#16810426 | C2 | semidirect |
| 6. #20272804 | C2 | semidirect |
| 7. C53×#1952 | C2 | semidirect |
| 180. #1952 | D53 | semidirect |
| 207. C53 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285209 | 2 |
| C2×#16810438 | 2 |
| C2×#16810429 | 2 |
| #20276425 | 2 |
| C2×#16810426 | 2 |
| #20272804 | 2 |
| C53×#1952 | 2 |
| #13412 | 53 |