Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 91 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×#16810401 | C2 | semidirect |
| 3. #20272747 | C2 | direct (N × H) |
| 4. C2×C53×#347 | C2 | semidirect |
| 15. #16810401 | C22 | semidirect |
| 19. C53×#347 | C22 | semidirect |
| 121. C2×#347 | D53 | semidirect |
| 125. C2×C53 | #1355 | semidirect |
| 142. #347 | C2×D53 | semidirect |
| 143. C53 | C2×#1355 | semidirect |
| 245. C2 | #20272747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810988 | 2 |
| C2×#16810401 | 2 |
| #20272747 | 2 |
| C2×C53×#347 | 2 |
| C2×#1355 | 53 |