Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #11719287 | C2 | semidirect |
| 2. C4×C13×Q16 | C2 | semidirect |
| 3. #11718852 | C2 | semidirect |
| 4. #11718849 | C2 | semidirect |
| 5. #11718687 | C2 | semidirect |
| 7. #11718535 | C2 | semidirect |
| 8. #11718473 | C2 | semidirect |
| 9. #11718456 | C2 | semidirect |
| 10. C4×D104 | C2 | semidirect |
| 11. #11718350 | C2 | semidirect |
| 104. C4×Q16 | D13 | semidirect |
| 188. C13 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719287 | 2 |
| C4×C13×Q16 | 2 |
| #11718852 | 2 |
| #11718849 | 2 |
| #11718687 | 2 |
| #11718544 | 2 |
| #11718535 | 2 |
| #11718473 | 2 |
| #11718456 | 2 |
| C4×D104 | 2 |
| #11718350 | 2 |
| #3175 | 13 |