Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
216 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11718586 | C2 | semidirect |
| 3. #11718585 | C2 | semidirect |
| 4. Q8⋊#1055 | C2 | semidirect |
| 5. D4⋊#1055 | C2 | semidirect |
| 142. C13 | #1495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| #11718586 | 2 |
| #11718585 | 2 |
| Q8⋊#1055 | 2 |
| D4⋊#1055 | 2 |
| #1495 | 13 |