Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11718511 | C2 | semidirect |
| 4. C8×Dic26 | C2 | semidirect |
| 5. C13×#334 | C2 | semidirect |
| 7. #11718073 | C2 | semidirect |
| 65. #334 | D13 | semidirect |
| 116. C13 | #1678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718511 | 2 |
| #11718509 | 2 |
| #11718355 | 2 |
| C8×Dic26 | 2 |
| C13×#334 | 2 |
| #11718077 | 2 |
| #11718073 | 2 |
| #1678 | 13 |