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. #20273114 | C2 | semidirect |
| 5. #20272611 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#1517 | C2 | semidirect |
| 11. #16810825 | C4 | semidirect |
| 12. #16810815 | C4 | semidirect |
| 191. #1517 | 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 |
|---|---|
| #20284175 | 2 |
| #20283755 | 2 |
| #20274722 | 2 |
| #20273114 | 2 |
| #20272611 | 2 |
| #20272573 | 2 |
| C53×#1517 | 2 |
| #9309 | 53 |