Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3754 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 3754 conjugacy classes of subgroups — too many to draw. Only its 555 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×#16810597 | C2 | semidirect |
| 2. #20277307 | C2 | semidirect |
| 3. #20274663 | C2 | semidirect |
| 5. C2×#13133176 | C22 | semidirect |
| 6. C22×C4⋊Dic53 | C22 | semidirect |
| 8. C2×#13133132 | C22 | semidirect |
| 11. #16810503 | C22 | semidirect |
| 14. C53×#585 | C4 | semidirect |
| 70. C2×Q8×C53 | C22⋊C4 | semidirect |
| 79. C2×D4×C53 | C22⋊C4 | semidirect |
| 87. C22×C4×C53 | C22⋊C4 | semidirect |
| 168. #585 | Dic53 | semidirect |
| 182. C53 | #20610 | semidirect |
| 233. C2×Q8 | C22⋊Dic53 | semidirect |
| 242. C2×D4 | C22⋊Dic53 | semidirect |
| 253. C22×C4 | C22⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810597 | 2 |
| #20277307 | 2 |
| #20274663 | 2 |
| C2×C53×#585 | 2 |
| #20610 | 53 |