Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
15150 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 15150 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C25×Dic53 | C2 | semidirect |
| 3. C22×#13133201 | C2 | direct (N × H) |
| 4. C23×C4⋊Dic53 | C2 | semidirect |
| 5. C23×#11719921 | C2 | semidirect |
| 6. C23×C22⋊C4×C53 | C2 | semidirect |
| 13. C24×Dic53 | C22 | semidirect |
| 14. C2×#13133201 | C22 | direct (N × H) |
| 15. C22×C4⋊Dic53 | C22 | semidirect |
| 16. C22×#11719921 | C22 | semidirect |
| 19. C22×C22⋊C4×C53 | C22 | semidirect |
| 30. C23×Dic53 | C23 | semidirect |
| 31. #13133201 | C23 | direct (N × H) |
| 32. C2×C4⋊Dic53 | C23 | semidirect |
| 33. C2×#11719921 | C23 | semidirect |
| 40. C2×C22⋊C4×C53 | C23 | semidirect |
| 61. C22×Dic53 | C24 | semidirect |
| 62. C22⋊C4×C53 | C24 | semidirect |
| 63. #11719921 | C24 | semidirect |
| 64. C4⋊Dic53 | C24 | semidirect |
| 67. C23×C53 | #123 | semidirect |
| 88. C22×C53 | C2×#123 | semidirect |
| 104. C23×C22⋊C4 | D53 | semidirect |
| 106. C2×C53 | C22×#123 | semidirect |
| 122. C22×C22⋊C4 | C2×D53 | semidirect |
| 123. C53 | C23×#123 | semidirect |
| 144. C2×C22⋊C4 | C22×D53 | semidirect |
| 168. C22⋊C4 | C23×D53 | semidirect |
| 175. C23 | #13133201 | direct (N × H) |
| 194. C22 | C2×#13133201 | direct (N × H) |
| 204. C2 | C22×#13133201 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C22⋊D53 | 2 |
| C25×Dic53 | 2 |
| C22×#13133201 | 2 |
| C23×C4⋊Dic53 | 2 |
| C23×#11719921 | 2 |
| C23×C22⋊C4×C53 | 2 |
| C23×#123 | 53 |