Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
652 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20273053 | C2 | semidirect |
| 3. #20272711 | C2 | semidirect |
| 4. C4×#99×C53 | C2 | semidirect |
| 5. C2×#13133214 | C4 | semidirect |
| 10. #16810532 | C4 | semidirect |
| 13. C4×C4⋊Dic53 | C4 | semidirect |
| 179. C4×#99 | D53 | semidirect |
| 205. C53 | #11776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279661 | 2 |
| #20273053 | 2 |
| #20272711 | 2 |
| C4×#99×C53 | 2 |
| #11776 | 53 |