Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
330 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 152 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. #11719158 | C2 | semidirect |
| 3. Q8×#1057 | C2 | semidirect |
| 4. #11719080 | C2 | semidirect |
| 6. #11719074 | C2 | semidirect |
| 138. C13 | #2986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| #11719158 | 2 |
| Q8×#1057 | 2 |
| #11719080 | 2 |
| #11719077 | 2 |
| #11719074 | 2 |
| #11719051 | 2 |
| #2986 | 13 |