Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. #20290149 | C2 | semidirect |
| 4. #20290025 | C2 | semidirect |
| 5. #20289605 | C2 | semidirect |
| 6. #20289570 | C2 | semidirect |
| 26. #16810914 | C4 | semidirect |
| 27. #16810913 | C4 | semidirect |
| 28. #16810900 | C4 | semidirect |
| 32. C53×#474 | C4 | semidirect |
| 228. #474 | #6157 | semidirect |
| 246. C53 | #9307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291578 | 2 |
| #20290585 | 2 |
| #20290149 | 2 |
| #20290025 | 2 |
| #20289605 | 2 |
| #20289570 | 2 |
| #20284507 | 2 |
| #9307 | 53 |