Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16810405 | C2 | semidirect |
| 3. #20272705 | C2 | direct (N × H) |
| 4. C2×C53×#338 | C2 | semidirect |
| 15. #16810405 | C22 | semidirect |
| 19. C53×#338 | C22 | semidirect |
| 170. C2×#338 | D53 | semidirect |
| 176. C2×C53 | #1341 | semidirect |
| 193. #338 | C2×D53 | semidirect |
| 194. C53 | C2×#1341 | semidirect |
| 347. C2 | #20272705 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810876 | 2 |
| C2×#16810405 | 2 |
| #20272705 | 2 |
| C2×C53×#338 | 2 |
| C2×#1341 | 53 |