Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20273227 | C2 | semidirect |
| 5. #20272609 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#1986 | C2 | semidirect |
| 10. #16810900 | C4 | semidirect |
| 11. #16810825 | C4 | semidirect |
| 178. #1986 | D53 | semidirect |
| 210. C53 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20277353 | 2 |
| #20273227 | 2 |
| #20273159 | 2 |
| #20272609 | 2 |
| #20272571 | 2 |
| C53×#1986 | 2 |
| #9327 | 53 |