Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×#16811514 | C2 | semidirect |
| 4. #20289755 | C2 | semidirect |
| 14. #16811518 | C4 | semidirect |
| 15. C22⋊#11719910 | C4 | semidirect |
| 19. C22⋊#11719908 | C4 | semidirect |
| 20. #16810402 | C4 | semidirect |
| 21. C53×C22⋊C16 | C4 | semidirect |
| 36. C2×#11719910 | C2×C4 | semidirect |
| 51. C2×#11719908 | C2×C4 | semidirect |
| 53. C2×C16×C53 | C2×C4 | semidirect |
| 139. C22×C53 | #347 | semidirect |
| 147. C2×D53 | #347 | semidirect |
| 184. C22⋊C16 | #6157 | semidirect |
| 186. C53 | #12605 | semidirect |
| 214. C2×C16 | C2×#6157 | semidirect |
| 312. C22 | #16811514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133271 | 2 |
| #20290943 | 2 |
| C2×#16811514 | 2 |
| #20289755 | 2 |
| #20276324 | 2 |
| #12605 | 53 |