Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1486 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 3. C2×#16810414 | C2 | direct (N × H) |
| 5. C24×Dic53 | C4 | semidirect |
| 8. C2×#13133198 | C4 | semidirect |
| 13. C22×C22⋊Dic53 | C4 | semidirect |
| 16. #16810414 | C22 | direct (N × H) |
| 27. C23×Dic53 | C2×C4 | semidirect |
| 31. #13133198 | C2×C4 | semidirect |
| 40. C2×C22⋊Dic53 | C2×C4 | semidirect |
| 97. C22×Dic53 | C22×C4 | semidirect |
| 106. C22⋊Dic53 | C22×C4 | semidirect |
| 173. C22×C53 | #352 | semidirect |
| 192. C2×C53 | C2×#352 | semidirect |
| 210. C53 | C22×#352 | semidirect |
| 362. C22 | #16810414 | direct (N × H) |
| 377. C2 | C2×#16810414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133198 | 2 |
| C22×#13133132 | 2 |
| C2×#16810414 | 2 |
| C22×#100×C53 | 2 |
| C22×#352 | 53 |