Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 164 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. #11719119 | C2 | semidirect |
| 3. C2×C4⋊#1057 | C2 | semidirect |
| 4. #11719080 | C2 | semidirect |
| 5. #11719076 | C2 | semidirect |
| 6. #11719064 | C2 | semidirect |
| 7. #11719054 | C2 | semidirect |
| 8. #11719052 | C2 | semidirect |
| 63. C2×C4×C13 | M16 | semidirect |
| 167. C13 | #2989 | semidirect |
| 185. C2×C4 | #6118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719227 | 2 |
| #11719119 | 2 |
| C2×C4⋊#1057 | 2 |
| #11719080 | 2 |
| #11719076 | 2 |
| #11719064 | 2 |
| #11719054 | 2 |
| #11719052 | 2 |
| #2989 | 13 |