Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. #11719222 | C2 | semidirect |
| 5. #11718781 | C2 | semidirect |
| 6. M16×Dic13 | C2 | semidirect |
| 7. #11718665 | C2 | semidirect |
| 8. #11718429 | C2 | semidirect |
| 9. #11718426 | C2 | semidirect |
| 21. #88144 | C22 | semidirect |
| 22. #88142 | C22 | semidirect |
| 27. #88056 | C22 | semidirect |
| 28. #88055 | C22 | semidirect |
| 29. C8×Dic13 | C22 | semidirect |
| 30. #88050 | C22 | semidirect |
| 166. C13 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88190 | 2 |
| #11719222 | 2 |
| C13×#418 | 2 |
| #11718876 | 2 |
| #11718781 | 2 |
| M16×Dic13 | 2 |
| #11718665 | 2 |
| #11718429 | 2 |
| #11718426 | 2 |
| #3140 | 13 |