Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20273396 | C2 | semidirect |
| 5. #20272573 | C2 | semidirect |
| 6. #20272546 | C2 | semidirect |
| 7. C53×#1993 | C2 | semidirect |
| 10. #16811019 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 170. #1993 | D53 | semidirect |
| 200. C53 | #9287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285843 | 2 |
| #20283434 | 2 |
| #20273396 | 2 |
| #20273274 | 2 |
| #20272573 | 2 |
| #20272546 | 2 |
| C53×#1993 | 2 |
| #9287 | 53 |