Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. #11719162 | C2 | semidirect |
| 3. #11718304 | C2 | semidirect |
| 4. #11718261 | C2 | semidirect |
| 5. #11718258 | C2 | semidirect |
| 78. C13 | #2171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719162 | 2 |
| #11718857 | 2 |
| #11718304 | 2 |
| #11718261 | 2 |
| #11718258 | 2 |
| #2171 | 13 |