Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11719386 | C2 | semidirect |
| 2. C13×#495 | C2 | semidirect |
| 3. #11718852 | C2 | semidirect |
| 4. Q16×Dic13 | C2 | semidirect |
| 5. #11718826 | C2 | semidirect |
| 6. #11718824 | C2 | semidirect |
| 8. D8×Dic13 | C2 | semidirect |
| 9. #11718718 | C2 | semidirect |
| 10. C4×D104 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 101. #495 | D13 | semidirect |
| 192. C13 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719386 | 2 |
| C13×#495 | 2 |
| #11718852 | 2 |
| Q16×Dic13 | 2 |
| #11718826 | 2 |
| #11718824 | 2 |
| #11718812 | 2 |
| D8×Dic13 | 2 |
| #11718718 | 2 |
| C4×D104 | 2 |
| C8×Dic26 | 2 |
| #3396 | 13 |