Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 96 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. #20290893 | C2 | semidirect |
| 4. #20290229 | C2 | semidirect |
| 5. #20289611 | C2 | semidirect |
| 6. #20289584 | C2 | semidirect |
| 26. #16810908 | C4 | semidirect |
| 27. #16810904 | C4 | semidirect |
| 28. #16810900 | C4 | semidirect |
| 32. C53×#475 | C4 | semidirect |
| 223. #475 | #6157 | semidirect |
| 243. C53 | #9315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291633 | 2 |
| #20290893 | 2 |
| #20290590 | 2 |
| #20290229 | 2 |
| #20289611 | 2 |
| #20289584 | 2 |
| #20284525 | 2 |
| #9315 | 53 |