Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
222 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #11718780 | C2 | semidirect |
| 5. C2×#88055 | C2 | semidirect |
| 6. C13×#341 | C2 | semidirect |
| 7. #11718147 | C2 | semidirect |
| 16. #88061 | C4 | semidirect |
| 18. #88056 | C4 | semidirect |
| 78. #341 | D13 | semidirect |
| 138. C13 | #1938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88065 | 2 |
| #11718790 | 2 |
| #11718780 | 2 |
| #11718774 | 2 |
| C2×#88055 | 2 |
| C13×#341 | 2 |
| #11718147 | 2 |
| #1938 | 13 |