Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 173 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. #11718363 | C2 | semidirect |
| 6. #11718343 | C2 | semidirect |
| 7. #11718341 | C2 | semidirect |
| 38. C13×M16 | Q8 | semidirect |
| 75. C8×C13 | C2×Q8 | semidirect |
| 130. M16 | Dic26 | semidirect |
| 148. C13 | #3165 | semidirect |
| 167. C8 | C2×Dic26 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719175 | 2 |
| C2×#88123 | 2 |
| C4×C13×M16 | 2 |
| #11718782 | 2 |
| #11718363 | 2 |
| #11718343 | 2 |
| #11718341 | 2 |
| #3165 | 13 |