Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #20273278 | C2 | semidirect |
| 4. #20273215 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 12. #16810914 | C4 | semidirect |
| 13. #16810904 | C4 | semidirect |
| 32. #13133217 | C2×C4 | semidirect |
| 33. #13133217 | C2×C4 | semidirect |
| 67. C4⋊C8×C53 | C2×C4 | semidirect |
| 196. #1286 | D53 | semidirect |
| 224. C53 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284514 | 2 |
| #20277623 | 2 |
| #20273278 | 2 |
| #20273215 | 2 |
| #20273105 | 2 |
| #20272616 | 2 |
| C53×#1286 | 2 |
| #9175 | 53 |