Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
800 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 213 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×#88123 | C2 | semidirect |
| 6. #11718590 | C2 | semidirect |
| 7. #11718317 | C2 | semidirect |
| 44. C13×C22⋊C4 | Q8 | semidirect |
| 63. C2×C4×C13 | C2×Q8 | semidirect |
| 85. C22×C13 | C4⋊Q8 | semidirect |
| 141. C22⋊C4 | Dic26 | semidirect |
| 143. C13 | #2434 | semidirect |
| 164. C2×C4 | C2×Dic26 | semidirect |
| 171. C22 | #88123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic26 | 2 |
| C2×#88178 | 2 |
| C2×#88123 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718611 | 2 |
| #11718590 | 2 |
| #11718317 | 2 |
| #2434 | 13 |