Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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. #11719061 | C2 | semidirect |
| 3. #11719055 | C2 | semidirect |
| 4. #11718292 | C2 | semidirect |
| 6. C13×#127 | C4 | semidirect |
| 11. D4×Dic13 | C4 | semidirect |
| 13. #88123 | C4 | semidirect |
| 84. #127 | #261 | semidirect |
| 122. C13 | #1514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| #11719061 | 2 |
| #11719055 | 2 |
| #11718292 | 2 |
| #1514 | 13 |