Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 3. #20272825 | C2 | semidirect |
| 4. #20272815 | C2 | semidirect |
| 15. C53×#430 | C4 | semidirect |
| 135. #430 | Dic53 | semidirect |
| 143. C53 | #12875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810405 | 2 |
| #20274748 | 2 |
| #20272825 | 2 |
| #20272815 | 2 |
| C2×C53×#430 | 2 |
| #12875 | 53 |