Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
670 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×D848 | C2 | semidirect |
| 2. C2×#16810859 | C2 | semidirect |
| 3. C2×#16810425 | C2 | semidirect |
| 4. #20272807 | C2 | semidirect |
| 5. C2×C53×C22⋊C16 | C2 | semidirect |
| 26. C2×D424 | D4 | semidirect |
| 33. #13133151 | D4 | semidirect |
| 45. C2×C16×C53 | D4 | semidirect |
| 86. C23×C53 | D16 | semidirect |
| 142. C2×C22⋊C16 | D53 | semidirect |
| 164. C53 | #13304 | semidirect |
| 188. C2×C16 | C22⋊D53 | semidirect |
| 239. C23 | D848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810859 | 2 |
| C2×#16810425 | 2 |
| #20272807 | 2 |
| C2×C53×C22⋊C16 | 2 |
| #13304 | 53 |