Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 147 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×#16810425 | C2 | semidirect |
| 3. #20274744 | C2 | semidirect |
| 4. #20272807 | C2 | semidirect |
| 5. C22×M32×C53 | C2 | semidirect |
| 9. #16810859 | C4 | semidirect |
| 48. C2×C16×C53 | D4 | semidirect |
| 139. C22×M32 | D53 | semidirect |
| 165. C53 | #13061 | semidirect |
| 188. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810859 | 2 |
| C2×#16810425 | 2 |
| #20274744 | 2 |
| #20272807 | 2 |
| C22×M32×C53 | 2 |
| #13061 | 53 |