Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#88166 | C2 | semidirect |
| 2. C22×Dic52 | C2 | semidirect |
| 3. #11719303 | C2 | semidirect |
| 4. C13×#466 | C2 | semidirect |
| 5. #11718816 | C2 | semidirect |
| 6. C8×C22⋊D13 | C2 | semidirect |
| 7. #11718701 | C2 | semidirect |
| 8. #11718548 | C2 | semidirect |
| 9. #11718534 | C2 | semidirect |
| 10. #11718444 | C2 | semidirect |
| 11. #11718428 | C2 | semidirect |
| 78. Dic52 | D4 | semidirect |
| 117. #466 | D13 | semidirect |
| 128. C22×C13 | #135 | semidirect |
| 216. C13 | #3285 | semidirect |
| 256. C22 | #88166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88166 | 2 |
| C22×Dic52 | 2 |
| #11719303 | 2 |
| C13×#466 | 2 |
| #11718816 | 2 |
| C8×C22⋊D13 | 2 |
| #11718701 | 2 |
| #11718548 | 2 |
| #11718534 | 2 |
| #11718444 | 2 |
| #11718428 | 2 |
| #3285 | 13 |