Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
518 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 518 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 |
|---|---|---|
| 2. #20283755 | C2 | semidirect |
| 3. #20274722 | C2 | semidirect |
| 4. #20273274 | C2 | semidirect |
| 5. #20273115 | C2 | semidirect |
| 6. #20272610 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 12. #16810829 | C4 | semidirect |
| 13. #16810819 | C4 | semidirect |
| 194. #1286 | D53 | semidirect |
| 221. C53 | #9309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284181 | 2 |
| #20283755 | 2 |
| #20274722 | 2 |
| #20273274 | 2 |
| #20273115 | 2 |
| #20272610 | 2 |
| C53×#1286 | 2 |
| #9309 | 53 |