Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20290659 | C2 | semidirect |
| 4. #20290658 | C2 | semidirect |
| 5. #20289558 | C2 | semidirect |
| 6. #20289558 | C2 | semidirect |
| 128. C22⋊C4×C53 | M16 | semidirect |
| 136. C22⋊Dic53 | M16 | semidirect |
| 279. C53 | #8852 | semidirect |
| 387. C22⋊C4 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291566 | 2 |
| #20290688 | 2 |
| #20290659 | 2 |
| #20290658 | 2 |
| #20289558 | 2 |
| #99×Dic53 | 2 |
| #8852 | 53 |