Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20276450 | C2 | semidirect |
| 3. C2×#16810405 | C2 | semidirect |
| 4. #20272816 | C2 | semidirect |
| 5. C53×#2911 | C2 | semidirect |
| 9. #16810881 | C4 | semidirect |
| 10. #16810876 | C4 | semidirect |
| 24. C2×Dic212 | C2×C4 | semidirect |
| 26. C2×D424 | C2×C4 | semidirect |
| 37. #13133149 | C2×C4 | semidirect |
| 57. #106×C53 | D4 | semidirect |
| 157. #2911 | D53 | semidirect |
| 182. C53 | #13008 | semidirect |
| 217. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284324 | 2 |
| #20276450 | 2 |
| C2×#16810405 | 2 |
| #20272816 | 2 |
| C53×#2911 | 2 |
| #13008 | 53 |