Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 1. #20291610 | C2 | semidirect |
| 2. #20290019 | C2 | semidirect |
| 5. #20289555 | C2 | semidirect |
| 6. #20289541 | C2 | semidirect |
| 46. C2×#11719913 | C8 | semidirect |
| 210. C53 | #9090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291610 | 2 |
| #20290019 | 2 |
| #20290016 | 2 |
| #20289956 | 2 |
| #20289555 | 2 |
| #20289541 | 2 |
| C2×#16810722 | 2 |
| #9090 | 53 |