Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 5. #11718683 | C2 | semidirect |
| 6. #11718683 | C2 | semidirect |
| 7. #11718682 | C2 | semidirect |
| 8. #11718681 | C2 | semidirect |
| 43. C2×Q8×C13 | Q8 | semidirect |
| 160. C2×Q8 | Dic26 | semidirect |
| 191. C13 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#519 | 2 |
| #11719224 | 2 |
| #11718886 | 2 |
| C2×#88075 | 2 |
| #11718683 | 2 |
| #11718682 | 2 |
| #11718681 | 2 |
| #11718660 | 2 |
| #11718659 | 2 |
| #11718656 | 2 |
| #3082 | 13 |