Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #11718755 | C2 | semidirect |
| 4. #11718754 | C2 | semidirect |
| 5. #11718713 | C2 | semidirect |
| 6. #11718711 | C2 | semidirect |
| 7. #11718692 | C2 | semidirect |
| 8. C4×#6107 | C2 | semidirect |
| 10. #11718665 | C2 | semidirect |
| 11. #11718657 | C2 | semidirect |
| 197. C13 | #3328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#556 | 2 |
| D4×Dic26 | 2 |
| #11718755 | 2 |
| #11718754 | 2 |
| #11718713 | 2 |
| #11718711 | 2 |
| #11718692 | 2 |
| C4×#6107 | 2 |
| #11718673 | 2 |
| #11718665 | 2 |
| #11718657 | 2 |
| #3328 | 13 |