Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. C2×#16811064 | C2 | semidirect |
| 3. C2×#16810432 | C2 | semidirect |
| 4. #20272799 | C2 | semidirect |
| 5. C53×#1971 | C2 | semidirect |
| 43. #13133157 | D4 | semidirect |
| 49. C2×Q16×C53 | D4 | semidirect |
| 152. #1971 | D53 | semidirect |
| 175. C53 | #13342 | semidirect |
| 189. C2×Q16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20285161 | 2 |
| C2×#16810432 | 2 |
| #20272799 | 2 |
| C53×#1971 | 2 |
| #13342 | 53 |