Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 530 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. #20275543 | C2 | semidirect |
| 3. #20273471 | C2 | semidirect |
| 4. #20273167 | C2 | semidirect |
| 5. C4×#97×C53 | C2 | semidirect |
| 7. #16811028 | C4 | semidirect |
| 8. #16811000 | C4 | semidirect |
| 9. #16810970 | C4 | semidirect |
| 102. C8×C53 | #104 | semidirect |
| 122. C4×#97 | D53 | semidirect |
| 144. C53 | #9849 | semidirect |
| 228. C8 | #13133145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| #20275543 | 2 |
| #20273471 | 2 |
| #20273167 | 2 |
| C4×#97×C53 | 2 |
| #9849 | 53 |