Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 111 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×C22⋊#11719908 | C2 | semidirect |
| 3. #20272732 | C2 | semidirect |
| 4. #20272729 | C2 | semidirect |
| 5. C2×C53×#341 | C2 | semidirect |
| 166. C2×#341 | D53 | semidirect |
| 193. C53 | #11709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284296 | 2 |
| C2×C22⋊#11719908 | 2 |
| #20272732 | 2 |
| #20272729 | 2 |
| C2×C53×#341 | 2 |
| #11709 | 53 |