Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16810381 | C2 | semidirect |
| 3. #20272710 | C2 | semidirect |
| 4. #20272707 | C2 | semidirect |
| 5. C2×C53×#349 | C2 | semidirect |
| 185. C2×#349 | D53 | semidirect |
| 213. C53 | #11688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284324 | 2 |
| C2×#16810381 | 2 |
| #20272710 | 2 |
| #20272707 | 2 |
| C2×C53×#349 | 2 |
| #11688 | 53 |