Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. #20290943 | C2 | semidirect |
| 2. #20290592 | C2 | semidirect |
| 3. #20289703 | C2 | semidirect |
| 4. #20289701 | C2 | semidirect |
| 14. #16810861 | C4 | semidirect |
| 16. #16810856 | C4 | semidirect |
| 20. #16810661 | C4 | semidirect |
| 22. C2×#135×C53 | C4 | semidirect |
| 182. C2×#135 | #6157 | semidirect |
| 199. C53 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290943 | 2 |
| #20290592 | 2 |
| #20289703 | 2 |
| #20289701 | 2 |
| #20284292 | 2 |
| #11890 | 53 |