Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20290922 | C2 | semidirect |
| 3. C4×#13133287 | C2 | semidirect |
| 4. #20289789 | C2 | semidirect |
| 9. #16811541 | C4 | semidirect |
| 26. #13133292 | C2×C4 | semidirect |
| 29. #13133287 | C2×C4 | semidirect |
| 156. Dic53 | #361 | semidirect |
| 187. C53 | C4×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811541 | 2 |
| #20290922 | 2 |
| C4×#13133287 | 2 |
| #20289789 | 2 |
| C4×D8×D53 | 2 |
| C4×#361 | 53 |