Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
33214 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 3307 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. C23×C22⋊Dic53 | C2 | semidirect |
| 2. C2×#16810479 | C2 | direct (N × H) |
| 4. C24×Dic53 | C22 | semidirect |
| 6. C22×C22⋊Dic53 | C22 | semidirect |
| 7. #16810479 | C22 | direct (N × H) |
| 9. C26×C53 | C4 | semidirect |
| 13. C23×Dic53 | C23 | semidirect |
| 15. C2×C22⋊Dic53 | C23 | semidirect |
| 21. C25×C53 | C2×C4 | semidirect |
| 33. C24×C53 | C22⋊C4 | semidirect |
| 36. C24×C53 | C22×C4 | semidirect |
| 43. C22×Dic53 | C24 | semidirect |
| 53. C23×C53 | C2×C22⋊C4 | semidirect |
| 67. C22×C53 | #379 | semidirect |
| 69. C22×C53 | C22×C22⋊C4 | semidirect |
| 78. C2×C53 | C2×#379 | semidirect |
| 82. C26 | Dic53 | semidirect |
| 89. C53 | C22×#379 | semidirect |
| 95. C25 | C2×Dic53 | semidirect |
| 111. C24 | C22⋊Dic53 | semidirect |
| 114. C24 | C22×Dic53 | semidirect |
| 131. C23 | C2×C22⋊Dic53 | semidirect |
| 144. C22 | #16810479 | direct (N × H) |
| 146. C22 | C22×C22⋊Dic53 | semidirect |
| 152. C2 | C2×#16810479 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊Dic53 | 2 |
| C2×#16810479 | 2 |
| C27×C53 | 2 |
| C22×#379 | 53 |