Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
344 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 2. #11719129 | C2 | semidirect |
| 3. #11719125 | C2 | semidirect |
| 4. #11718297 | C2 | semidirect |
| 16. #88112 | C22 | semidirect |
| 17. #88112 | C22 | semidirect |
| 145. C13 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88194 | 2 |
| #11719129 | 2 |
| #11719125 | 2 |
| #11718297 | 2 |
| #1545 | 13 |