Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4×C13×Q16 | C2 | semidirect |
| 3. #11718850 | C2 | semidirect |
| 4. #11718683 | C2 | semidirect |
| 5. #11718542 | C2 | semidirect |
| 6. #11718475 | C2 | semidirect |
| 7. #11718470 | C2 | semidirect |
| 9. #11718344 | C2 | semidirect |
| 86. C4×Q16 | D13 | semidirect |
| 157. C13 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719286 | 2 |
| C4×C13×Q16 | 2 |
| #11718850 | 2 |
| #11718683 | 2 |
| #11718542 | 2 |
| #11718475 | 2 |
| #11718470 | 2 |
| #11718349 | 2 |
| #11718344 | 2 |
| #3352 | 13 |