Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #11719290 | C2 | semidirect |
| 2. #11719247 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718829 | C2 | semidirect |
| 5. #11718692 | C2 | semidirect |
| 7. #11718513 | C2 | semidirect |
| 8. #11718459 | C2 | semidirect |
| 9. #11718448 | C2 | semidirect |
| 10. #11718354 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 114. C4×SD16 | D13 | semidirect |
| 201. C13 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719290 | 2 |
| #11719247 | 2 |
| C4×C13×SD16 | 2 |
| #11718829 | 2 |
| #11718692 | 2 |
| #11718676 | 2 |
| #11718513 | 2 |
| #11718459 | 2 |
| #11718448 | 2 |
| #11718354 | 2 |
| C8×Dic26 | 2 |
| #3394 | 13 |