Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
738 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 738 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. #20275663 | C2 | semidirect |
| 4. #20272556 | C2 | semidirect |
| 9. #16810995 | C4 | semidirect |
| 28. #13133217 | C2×C4 | semidirect |
| 33. C4×#88322 | C2×C4 | semidirect |
| 74. C4⋊C4×C53 | SD16 | semidirect |
| 172. C53 | #9064 | semidirect |
| 236. C4⋊C4 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810995 | 2 |
| #20275663 | 2 |
| C2×#16810367 | 2 |
| #20272556 | 2 |
| C53×#2366 | 2 |
| #9064 | 53 |