Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2502 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 371 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×#16810491 | C2 | semidirect |
| 3. #20272955 | C2 | semidirect |
| 4. C2×C53×#383 | C2 | semidirect |
| 8. C2×#13133214 | C4 | semidirect |
| 47. C42×C53 | C22⋊C4 | semidirect |
| 83. C2×#383 | D53 | semidirect |
| 100. C53 | #14661 | semidirect |
| 134. C42 | #11719921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133214 | 2 |
| C2×#16810491 | 2 |
| #20272955 | 2 |
| C2×C53×#383 | 2 |
| #14661 | 53 |