Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. C4×C13×Q16 | C2 | semidirect |
| 4. #11718850 | C2 | semidirect |
| 5. #11718682 | C2 | semidirect |
| 6. #11718681 | C2 | semidirect |
| 7. #11718542 | C2 | semidirect |
| 8. #11718476 | C2 | semidirect |
| 9. #11718466 | C2 | semidirect |
| 11. #11718341 | C2 | semidirect |
| 106. C4×Q16 | D13 | semidirect |
| 189. C13 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719289 | 2 |
| #11719284 | 2 |
| C4×C13×Q16 | 2 |
| #11718850 | 2 |
| #11718682 | 2 |
| #11718681 | 2 |
| #11718542 | 2 |
| #11718476 | 2 |
| #11718466 | 2 |
| #11718349 | 2 |
| #11718341 | 2 |
| #3356 | 13 |