Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2070 conjugacy classes of subgroups; only the 651 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 651 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. #20272980 | C2 | semidirect |
| 9. C2×#95×C53 | C4 | semidirect |
| 33. C22×C4×C53 | C4⋊C4 | semidirect |
| 95. C2×#95 | Dic53 | semidirect |
| 97. C53 | #14353 | semidirect |
| 123. C22×C4 | C4⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810483 | 2 |
| #20272980 | 2 |
| C22×#95×C53 | 2 |
| #14353 | 53 |