Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #11719275 | C2 | semidirect |
| 3. C4×C13×Q16 | C2 | semidirect |
| 4. #11718846 | C2 | semidirect |
| 6. #11718681 | C2 | semidirect |
| 7. #11718552 | C2 | semidirect |
| 8. #11718461 | C2 | semidirect |
| 9. #11718449 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 108. C4×Q16 | D13 | semidirect |
| 190. C13 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719290 | 2 |
| #11719275 | 2 |
| C4×C13×Q16 | 2 |
| #11718846 | 2 |
| #11718688 | 2 |
| #11718681 | 2 |
| #11718552 | 2 |
| #11718461 | 2 |
| #11718449 | 2 |
| #11718355 | 2 |
| C8×Dic26 | 2 |
| #3365 | 13 |