Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #11719530 | C2 | semidirect |
| 3. C2×#88163 | C2 | semidirect |
| 4. C22×Dic52 | C2 | semidirect |
| 5. C13×#408 | C2 | semidirect |
| 6. #11718781 | C2 | semidirect |
| 7. #11718774 | C2 | semidirect |
| 8. #11718400 | C2 | semidirect |
| 9. #11718394 | C2 | semidirect |
| 129. #408 | D13 | semidirect |
| 223. C13 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88257 | 2 |
| #11719530 | 2 |
| C2×#88163 | 2 |
| C22×Dic52 | 2 |
| C13×#408 | 2 |
| #11718781 | 2 |
| #11718774 | 2 |
| #11718400 | 2 |
| #11718394 | 2 |
| #3011 | 13 |