Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20276406 | C2 | semidirect |
| 3. #20276366 | C2 | semidirect |
| 4. #20274515 | C2 | semidirect |
| 5. C53×#1813 | C2 | semidirect |
| 6. C22×D424 | C4 | semidirect |
| 12. #16810661 | C4 | semidirect |
| 13. #16810629 | C4 | semidirect |
| 164. #1813 | D53 | semidirect |
| 190. C53 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284363 | 2 |
| #20276406 | 2 |
| #20276366 | 2 |
| #20274515 | 2 |
| C53×#1813 | 2 |
| #13234 | 53 |