Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11719175 | C2 | semidirect |
| 3. C13×#431 | C2 | semidirect |
| 4. #11718512 | C2 | semidirect |
| 5. #11718510 | C2 | semidirect |
| 6. #11718507 | C2 | semidirect |
| 7. #11718502 | C2 | semidirect |
| 9. #11718384 | C2 | semidirect |
| 10. C4×Dic52 | C2 | semidirect |
| 11. C4×#6095 | C2 | semidirect |
| 123. #431 | D13 | semidirect |
| 218. C13 | #3107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6127 | 2 |
| #11719175 | 2 |
| C13×#431 | 2 |
| #11718512 | 2 |
| #11718510 | 2 |
| #11718507 | 2 |
| #11718502 | 2 |
| #11718394 | 2 |
| #11718384 | 2 |
| C4×Dic52 | 2 |
| C4×#6095 | 2 |
| #3107 | 13 |