Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
544 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 6. #11718590 | C2 | semidirect |
| 7. #11718589 | C2 | semidirect |
| 8. #11718322 | C2 | semidirect |
| 9. #11718317 | C2 | semidirect |
| 34. C22×C4×C13 | Q8 | semidirect |
| 50. C13×C22⋊C4 | Q8 | semidirect |
| 158. C22×C4 | Dic26 | semidirect |
| 170. C22⋊C4 | Dic26 | semidirect |
| 173. C13 | #2549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88132 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718873 | 2 |
| C2×#88071 | 2 |
| #11718611 | 2 |
| #11718590 | 2 |
| #11718589 | 2 |
| #11718322 | 2 |
| #11718317 | 2 |
| #2549 | 13 |