Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 147 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×#16810401 | C2 | semidirect |
| 4. #20272796 | C2 | semidirect |
| 5. C2×C53×#347 | C2 | semidirect |
| 15. #16810404 | C4 | semidirect |
| 36. #13133157 | C2×C4 | semidirect |
| 46. M32×C53 | C2×C4 | semidirect |
| 133. C2×#347 | D53 | semidirect |
| 154. C53 | #12607 | semidirect |
| 176. M32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810575 | 2 |
| C2×#16810404 | 2 |
| C2×#16810401 | 2 |
| #20272796 | 2 |
| C2×C53×#347 | 2 |
| #12607 | 53 |