Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
640 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20274703 | C2 | semidirect |
| 3. #20273284 | C2 | semidirect |
| 4. #20272595 | C2 | semidirect |
| 5. C53×#2972 | C2 | semidirect |
| 9. #16810553 | C4 | semidirect |
| 10. #16810548 | C4 | semidirect |
| 11. #16810540 | C4 | semidirect |
| 12. #16810532 | C4 | semidirect |
| 63. C22⋊C8×C53 | D4 | semidirect |
| 210. #2972 | D53 | semidirect |
| 243. C53 | #9384 | semidirect |
| 276. C22⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279671 | 2 |
| #20274703 | 2 |
| #20273284 | 2 |
| #20272595 | 2 |
| C53×#2972 | 2 |
| #9384 | 53 |