Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16810856 | C2 | semidirect |
| 2. C2×#16810424 | C2 | semidirect |
| 3. C2×#16810402 | C2 | semidirect |
| 4. #20272807 | C2 | semidirect |
| 5. C22×D16×C53 | C2 | semidirect |
| 33. #13133151 | D4 | semidirect |
| 41. C2×D8×C53 | D4 | semidirect |
| 45. C2×C16×C53 | D4 | semidirect |
| 94. C22×D53 | D16 | semidirect |
| 139. C22×D16 | D53 | semidirect |
| 164. C53 | #13304 | semidirect |
| 173. C2×D8 | C22⋊D53 | semidirect |
| 188. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810856 | 2 |
| C2×#16810424 | 2 |
| C2×#16810402 | 2 |
| #20272807 | 2 |
| C22×D16×C53 | 2 |
| #13304 | 53 |