Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#16810456 | C2 | semidirect |
| 2. C22×#13133123 | C2 | semidirect |
| 4. #20272910 | C2 | semidirect |
| 5. #20272852 | C2 | semidirect |
| 6. #20272848 | C2 | semidirect |
| 7. C53×C22⋊C32 | C2 | semidirect |
| 32. #13133123 | D4 | semidirect |
| 80. C22×C53 | M64 | semidirect |
| 96. C22⋊C32 | D53 | semidirect |
| 116. C53 | #13645 | semidirect |
| 178. C22 | #16810456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810456 | 2 |
| C22×#13133123 | 2 |
| C16×C22⋊D53 | 2 |
| #20272910 | 2 |
| #20272852 | 2 |
| #20272848 | 2 |
| C53×C22⋊C32 | 2 |
| #13645 | 53 |