Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
5502 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 5502 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 |
|---|---|---|
| 2. C2×#16810493 | C2 | direct (N × H) |
| 7. #16810493 | C22 | direct (N × H) |
| 9. C22×C42×C53 | C4 | semidirect |
| 20. C2×C42×C53 | C2×C4 | semidirect |
| 26. C22×C4×C53 | C4⋊C4 | semidirect |
| 34. C42×C53 | C22×C4 | semidirect |
| 43. C2×C4×C53 | C2×C4⋊C4 | semidirect |
| 50. C22×C53 | #384 | semidirect |
| 57. C4×C53 | C22×C4⋊C4 | semidirect |
| 62. C2×C53 | C2×#384 | semidirect |
| 70. C22×C42 | Dic53 | semidirect |
| 73. C53 | C22×#384 | semidirect |
| 83. C2×C42 | C2×Dic53 | semidirect |
| 92. C22×C4 | C4⋊Dic53 | semidirect |
| 98. C42 | C22×Dic53 | semidirect |
| 108. C2×C4 | C2×C4⋊Dic53 | semidirect |
| 112. C22 | #16810493 | direct (N × H) |
| 120. C4 | C22×C4⋊Dic53 | semidirect |
| 121. C2 | C2×#16810493 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic53 | 2 |
| C2×#16810493 | 2 |
| C23×C42×C53 | 2 |
| C22×#384 | 53 |