Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
774 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 206 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×#88240 | C2 | semidirect |
| 3. #11719159 | C2 | semidirect |
| 4. #11719127 | C2 | semidirect |
| 5. D13⋊(C22⋊C8) | C2 | semidirect |
| 15. C2×#6118 | C22 | semidirect |
| 16. C2×D13⋊C8 | C22 | semidirect |
| 19. #88111 | C22 | semidirect |
| 20. #88111 | C22 | semidirect |
| 75. C22×C13 | #131 | semidirect |
| 132. C13 | #2880 | semidirect |
| 165. C22 | #88240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6131 | 2 |
| C2×#88240 | 2 |
| #11719159 | 2 |
| #11719127 | 2 |
| D13⋊(C22⋊C8) | 2 |
| #2880 | 13 |