Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#16810416 | C2 | semidirect |
| 2. #20274703 | C2 | semidirect |
| 3. C4×#13133132 | C2 | semidirect |
| 12. C2×#127×C53 | C4 | semidirect |
| 19. C53×#390 | C4 | semidirect |
| 20. C4×C4⋊C4×C53 | C4 | semidirect |
| 27. #13133132 | D4 | semidirect |
| 191. C4×C53 | #353 | semidirect |
| 207. C2×#127 | Dic53 | semidirect |
| 216. #390 | Dic53 | semidirect |
| 218. C4×C4⋊C4 | Dic53 | semidirect |
| 223. C53 | #13223 | semidirect |
| 395. C4 | #16810416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| #20274703 | 2 |
| C4×#13133132 | 2 |
| C53×#2541 | 2 |
| #13223 | 53 |