Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 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. C2×C22⋊#1057 | C2 | semidirect |
| 3. #11719130 | C2 | semidirect |
| 4. #11719127 | C2 | semidirect |
| 5. #11719064 | C2 | semidirect |
| 9. C22×#1057 | C22 | semidirect |
| 10. C2×#6118 | C22 | semidirect |
| 18. C22⋊#1057 | C22 | semidirect |
| 19. #88111 | C22 | semidirect |
| 20. #88110 | C22 | semidirect |
| 21. C4⋊#1057 | C22 | semidirect |
| 48. C23×C13 | M16 | semidirect |
| 140. C13 | #2973 | semidirect |
| 147. C23 | #6118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88135 | 2 |
| C2×C22⋊#1057 | 2 |
| #11719130 | 2 |
| #11719127 | 2 |
| #11719064 | 2 |
| #2973 | 13 |