Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1946 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 259 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. C22×#13133132 | C2 | semidirect |
| 2. #20272938 | C2 | semidirect |
| 8. C23×D4×C53 | C4 | semidirect |
| 13. C22×C4⋊C4×C53 | C4 | semidirect |
| 14. C22×C22⋊C4×C53 | C4 | semidirect |
| 19. C2×C22⋊Dic53 | D4 | semidirect |
| 137. C2×C4×C53 | #99 | semidirect |
| 183. C23×D4 | Dic53 | semidirect |
| 188. C22×C4⋊C4 | Dic53 | semidirect |
| 190. C22×C22⋊C4 | Dic53 | semidirect |
| 194. C53 | #10980 | semidirect |
| 322. C2×C4 | #13133132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133132 | 2 |
| #20272938 | 2 |
| C22×#121×C53 | 2 |
| #10980 | 53 |