Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 436 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. #20283711 | C2 | semidirect |
| 3. #20273327 | C2 | semidirect |
| 4. #20273274 | C2 | semidirect |
| 5. #20272613 | C2 | semidirect |
| 6. #20272596 | C2 | semidirect |
| 7. C53×#1512 | C2 | semidirect |
| 9. #16811033 | C4 | semidirect |
| 10. #16811013 | C4 | semidirect |
| 11. #16810989 | C4 | semidirect |
| 12. #16810982 | C4 | semidirect |
| 206. #1512 | D53 | semidirect |
| 243. C53 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285414 | 2 |
| #20283711 | 2 |
| #20273327 | 2 |
| #20273274 | 2 |
| #20272613 | 2 |
| #20272596 | 2 |
| C53×#1512 | 2 |
| #9432 | 53 |