Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
508 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 165 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. #11718647 | C2 | semidirect |
| 7. #11718645 | C2 | semidirect |
| 8. #11718640 | C2 | semidirect |
| 34. C22×C4×C13 | Q8 | semidirect |
| 139. C22×C4 | Dic26 | semidirect |
| 153. C13 | #2627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×C4⋊C4 | 2 |
| C2×#88178 | 2 |
| #11718873 | 2 |
| #11718872 | 2 |
| #11718871 | 2 |
| #11718647 | 2 |
| #11718645 | 2 |
| #11718640 | 2 |
| #2627 | 13 |