Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 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. #11719284 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718834 | C2 | semidirect |
| 5. #11718692 | C2 | semidirect |
| 6. #11718669 | C2 | semidirect |
| 7. #11718523 | C2 | semidirect |
| 8. #11718477 | C2 | semidirect |
| 9. #11718432 | C2 | semidirect |
| 10. #11718349 | C2 | semidirect |
| 11. #11718342 | C2 | semidirect |
| 113. C4×SD16 | D13 | semidirect |
| 202. C13 | #3331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719284 | 2 |
| #11719260 | 2 |
| C4×C13×SD16 | 2 |
| #11718834 | 2 |
| #11718692 | 2 |
| #11718669 | 2 |
| #11718523 | 2 |
| #11718477 | 2 |
| #11718432 | 2 |
| #11718349 | 2 |
| #11718342 | 2 |
| #3331 | 13 |