Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C2×#88062 | C2 | semidirect |
| 5. C2×#88047 | C2 | semidirect |
| 6. C13×#343 | C2 | semidirect |
| 7. #11718146 | C2 | semidirect |
| 16. #88161 | C4 | semidirect |
| 89. #343 | D13 | semidirect |
| 159. C13 | #1816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88161 | 2 |
| #11718794 | 2 |
| C2×#88062 | 2 |
| #11718627 | 2 |
| C2×#88047 | 2 |
| C13×#343 | 2 |
| #11718146 | 2 |
| #1816 | 13 |