Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11719175 | C2 | semidirect |
| 3. C4×C13×M16 | C2 | semidirect |
| 4. #11718798 | C2 | semidirect |
| 6. #11718376 | C2 | semidirect |
| 7. #11718375 | C2 | semidirect |
| 8. #11718364 | C2 | semidirect |
| 9. #11718363 | C2 | semidirect |
| 10. C4×Dic52 | C2 | semidirect |
| 11. C4×#6095 | C2 | semidirect |
| 117. C4×M16 | D13 | semidirect |
| 210. C13 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| #11719175 | 2 |
| C4×C13×M16 | 2 |
| #11718798 | 2 |
| #11718795 | 2 |
| #11718376 | 2 |
| #11718375 | 2 |
| #11718364 | 2 |
| #11718363 | 2 |
| C4×Dic52 | 2 |
| C4×#6095 | 2 |
| #3172 | 13 |