Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11719285 | C2 | semidirect |
| 2. C4×C13×Q16 | C2 | semidirect |
| 3. #11718852 | C2 | semidirect |
| 4. #11718849 | C2 | semidirect |
| 5. C4×#6106 | C2 | semidirect |
| 7. #11718539 | C2 | semidirect |
| 8. #11718468 | C2 | semidirect |
| 9. #11718461 | C2 | semidirect |
| 10. C4×D104 | C2 | semidirect |
| 11. C4×C8×D13 | C2 | semidirect |
| 104. C4×Q16 | D13 | semidirect |
| 189. C13 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719285 | 2 |
| C4×C13×Q16 | 2 |
| #11718852 | 2 |
| #11718849 | 2 |
| C4×#6106 | 2 |
| #11718544 | 2 |
| #11718539 | 2 |
| #11718468 | 2 |
| #11718461 | 2 |
| C4×D104 | 2 |
| C4×C8×D13 | 2 |
| #3168 | 13 |