Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #20273278 | C2 | semidirect |
| 5. #20273119 | C2 | semidirect |
| 6. #20272610 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 11. #16810914 | C4 | semidirect |
| 12. #16810904 | C4 | semidirect |
| 176. #1286 | D53 | semidirect |
| 202. C53 | #9307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284514 | 2 |
| #20283755 | 2 |
| #20274722 | 2 |
| #20273278 | 2 |
| #20273119 | 2 |
| #20272610 | 2 |
| C53×#1286 | 2 |
| #9307 | 53 |