Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 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. #20283749 | C2 | semidirect |
| 3. #20274543 | C2 | semidirect |
| 4. #20273326 | C2 | semidirect |
| 5. #20272615 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#1502 | C2 | semidirect |
| 10. #16810910 | C4 | semidirect |
| 11. #16810910 | C4 | semidirect |
| 12. #16810815 | C4 | semidirect |
| 13. #16810815 | C4 | semidirect |
| 217. #1502 | D53 | semidirect |
| 253. C53 | #9163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284802 | 2 |
| #20283749 | 2 |
| #20274543 | 2 |
| #20273326 | 2 |
| #20272615 | 2 |
| #20272571 | 2 |
| C53×#1502 | 2 |
| #9163 | 53 |