Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 156 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. #11719145 | C2 | semidirect |
| 3. #11719129 | C2 | semidirect |
| 4. #11719128 | C2 | semidirect |
| 5. #11719080 | C2 | semidirect |
| 6. #11719065 | C2 | semidirect |
| 7. D13⋊(C4⋊C8) | C2 | semidirect |
| 8. #11719049 | C2 | semidirect |
| 81. C4×D13 | M16 | semidirect |
| 167. C13 | #2989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6129 | 2 |
| #11719145 | 2 |
| #11719129 | 2 |
| #11719128 | 2 |
| #11719080 | 2 |
| #11719065 | 2 |
| D13⋊(C4⋊C8) | 2 |
| #11719049 | 2 |
| #2989 | 13 |