Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
43678 conjugacy classes of subgroups; only the 10859 normal subgroups are shown.
This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 10859 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. C23×#11719921 | C2 | direct (N × H) |
| 4. C25×C4×C53 | C2 | semidirect |
| 7. C25×D53 | C4 | semidirect |
| 10. C24×Dic53 | C22 | semidirect |
| 11. C22×#11719921 | C22 | direct (N × H) |
| 14. C24×C4×C53 | C22 | semidirect |
| 18. C24×D53 | C2×C4 | semidirect |
| 21. C23×Dic53 | C23 | semidirect |
| 22. C2×#11719921 | C23 | direct (N × H) |
| 28. C23×C4×C53 | C23 | semidirect |
| 29. C24×C53 | C22⋊C4 | semidirect |
| 37. C23×D53 | C22×C4 | semidirect |
| 40. C22×C4×C53 | C24 | semidirect |
| 42. C22×Dic53 | C24 | semidirect |
| 43. #11719921 | C24 | direct (N × H) |
| 44. C23×C53 | C2×C22⋊C4 | semidirect |
| 52. C22×D53 | C23×C4 | semidirect |
| 55. C2×C4×C53 | C25 | semidirect |
| 57. C2×Dic53 | C25 | semidirect |
| 59. C22×C53 | C22×C22⋊C4 | semidirect |
| 67. C2×D53 | C24×C4 | semidirect |
| 72. C25×C4 | D53 | semidirect |
| 74. C2×C53 | C23×C22⋊C4 | semidirect |
| 87. C24×C4 | C2×D53 | semidirect |
| 89. C53 | C24×C22⋊C4 | semidirect |
| 102. C23×C4 | C22×D53 | semidirect |
| 109. C24 | #11719921 | direct (N × H) |
| 117. C22×C4 | C23×D53 | semidirect |
| 124. C23 | C2×#11719921 | direct (N × H) |
| 132. C2×C4 | C24×D53 | semidirect |
| 137. C22 | C22×#11719921 | direct (N × H) |
| 145. C2 | C23×#11719921 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×D53 | 2 |
| C25×Dic53 | 2 |
| C23×#11719921 | 2 |
| C25×C4×C53 | 2 |
| C24×C22⋊C4 | 53 |