Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20274711 | C2 | semidirect |
| 4. #20272841 | C2 | semidirect |
| 5. C53×#1801 | C2 | semidirect |
| 185. #1801 | D53 | semidirect |
| 211. C53 | #12803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277422 | 2 |
| C2×#16810419 | 2 |
| #20274711 | 2 |
| #20272841 | 2 |
| C53×#1801 | 2 |
| #12803 | 53 |