Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 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. #11719376 | C2 | semidirect |
| 3. Q16×Dic13 | C2 | semidirect |
| 4. #11718842 | C2 | semidirect |
| 5. #11718827 | C2 | semidirect |
| 6. #11718823 | C2 | semidirect |
| 9. #11718715 | C2 | semidirect |
| 10. C4×Dic52 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 186. C13 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719376 | 2 |
| C13×#495 | 2 |
| Q16×Dic13 | 2 |
| #11718842 | 2 |
| #11718827 | 2 |
| #11718823 | 2 |
| #11718816 | 2 |
| D8×Dic13 | 2 |
| #11718715 | 2 |
| C4×Dic52 | 2 |
| C8×Dic26 | 2 |
| #3393 | 13 |