Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #11719248 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718826 | C2 | semidirect |
| 5. #11718682 | C2 | semidirect |
| 7. #11718532 | C2 | semidirect |
| 8. #11718461 | C2 | semidirect |
| 9. #11718417 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 110. C4×SD16 | D13 | semidirect |
| 195. C13 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719290 | 2 |
| #11719248 | 2 |
| C4×C13×SD16 | 2 |
| #11718826 | 2 |
| #11718682 | 2 |
| #11718676 | 2 |
| #11718532 | 2 |
| #11718461 | 2 |
| #11718417 | 2 |
| #11718355 | 2 |
| C8×Dic26 | 2 |
| #3361 | 13 |