Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20275642 | C2 | semidirect |
| 3. C2×#16810367 | C2 | semidirect |
| 4. #20272556 | C2 | semidirect |
| 5. C53×#2366 | C2 | semidirect |
| 9. #16810999 | C4 | semidirect |
| 29. #13133214 | C2×C4 | semidirect |
| 35. C4×#88322 | C2×C4 | semidirect |
| 82. C4⋊C4×C53 | D8 | semidirect |
| 164. #2366 | D53 | semidirect |
| 189. C53 | #9061 | semidirect |
| 259. C4⋊C4 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810999 | 2 |
| #20275642 | 2 |
| C2×#16810367 | 2 |
| #20272556 | 2 |
| C53×#2366 | 2 |
| #9061 | 53 |