Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 202 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×#88106 | C2 | semidirect |
| 3. C22×#6092 | C2 | semidirect |
| 4. #11719096 | C2 | direct (N × H) |
| 5. C2×#88098 | C2 | semidirect |
| 6. C2×D13⋊C16 | C2 | semidirect |
| 14. #88106 | C22 | semidirect |
| 18. C2×#6092 | C22 | semidirect |
| 19. #88098 | C22 | semidirect |
| 20. D13⋊C16 | C22 | semidirect |
| 87. C2×C13 | #504 | semidirect |
| 109. C13 | C2×#504 | semidirect |
| 137. C2 | #11719096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88161 | 2 |
| C2×#88106 | 2 |
| C22×#6092 | 2 |
| #11719096 | 2 |
| C2×#88098 | 2 |
| C2×D13⋊C16 | 2 |
| C2×#504 | 13 |