Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 4. #11718780 | C2 | semidirect |
| 5. M16×Dic13 | C2 | semidirect |
| 6. #11718763 | C2 | semidirect |
| 7. C2×#88055 | C2 | semidirect |
| 8. #11718381 | C2 | semidirect |
| 9. #11718380 | C2 | semidirect |
| 149. C13 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic13 | 2 |
| C13×#408 | 2 |
| #11718895 | 2 |
| #11718780 | 2 |
| M16×Dic13 | 2 |
| #11718763 | 2 |
| C2×#88055 | 2 |
| #11718381 | 2 |
| #11718380 | 2 |
| #2923 | 13 |