Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 5. #11718843 | C2 | semidirect |
| 6. #11718842 | C2 | semidirect |
| 8. #11718454 | C2 | semidirect |
| 9. #11718453 | C2 | semidirect |
| 102. C2×Dic13 | Q16 | semidirect |
| 217. C13 | #3209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88198 | 2 |
| #11719327 | 2 |
| C13×#451 | 2 |
| #11718889 | 2 |
| #11718843 | 2 |
| #11718842 | 2 |
| #11718711 | 2 |
| #11718454 | 2 |
| #11718453 | 2 |
| #11718400 | 2 |
| #11718379 | 2 |
| #3209 | 13 |