Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
514 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16810363 | C2 | semidirect |
| 3. #20272862 | C2 | direct (N × H) |
| 4. C2×C53×#355 | C2 | semidirect |
| 15. #16810363 | C22 | semidirect |
| 19. C53×#355 | C22 | semidirect |
| 173. C2×#355 | D53 | semidirect |
| 180. C2×C53 | #1403 | semidirect |
| 195. #355 | C2×D53 | semidirect |
| 198. C53 | C2×#1403 | semidirect |
| 355. C2 | #20272862 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810800 | 2 |
| C2×#16810363 | 2 |
| #20272862 | 2 |
| C2×C53×#355 | 2 |
| C2×#1403 | 53 |