Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. #11718777 | C2 | semidirect |
| 4. #11718400 | C2 | semidirect |
| 5. #11718383 | C2 | semidirect |
| 16. C2×Dic52 | C22 | semidirect |
| 18. #88058 | C22 | semidirect |
| 19. #88056 | C22 | semidirect |
| 43. C23×C13 | Q16 | semidirect |
| 117. C13 | #3189 | semidirect |
| 120. C23 | Dic52 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88178 | 2 |
| C2×C13×C22⋊C8 | 2 |
| #11718777 | 2 |
| #11718400 | 2 |
| #11718383 | 2 |
| #3189 | 13 |