Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 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. C2×#16810432 | C2 | semidirect |
| 3. #20276326 | C2 | semidirect |
| 4. #20272822 | C2 | semidirect |
| 5. C2×C53×#427 | C2 | semidirect |
| 9. #16810864 | C4 | semidirect |
| 10. #16810859 | C4 | semidirect |
| 54. #106×C53 | D4 | semidirect |
| 153. C2×#427 | D53 | semidirect |
| 178. C53 | #13002 | semidirect |
| 210. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284296 | 2 |
| C2×#16810432 | 2 |
| #20276326 | 2 |
| #20272822 | 2 |
| C2×C53×#427 | 2 |
| #13002 | 53 |