Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
402 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 144 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. #11719146 | C2 | semidirect |
| 3. #11719145 | C2 | semidirect |
| 4. #11719144 | C2 | semidirect |
| 5. #11719127 | C2 | semidirect |
| 6. #11719126 | C2 | semidirect |
| 7. #11719077 | C2 | semidirect |
| 8. #11719066 | C2 | semidirect |
| 9. #11719064 | C2 | semidirect |
| 13. C2×#6122 | C22 | semidirect |
| 14. C22×#1057 | C22 | semidirect |
| 27. C22⋊#1057 | C22 | semidirect |
| 28. C22⋊#1057 | C22 | semidirect |
| 29. #88112 | C22 | semidirect |
| 34. #88110 | C22 | semidirect |
| 35. C4⋊#1057 | C22 | semidirect |
| 36. C4×#1057 | C22 | semidirect |
| 199. C13 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719311 | 2 |
| #11719146 | 2 |
| #11719145 | 2 |
| #11719144 | 2 |
| #11719127 | 2 |
| #11719126 | 2 |
| #11719077 | 2 |
| #11719066 | 2 |
| #11719064 | 2 |
| #2978 | 13 |