Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
292 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11719159 | C2 | semidirect |
| 3. C2×#88118 | C2 | semidirect |
| 4. #11719147 | C2 | semidirect |
| 5. C2×#88116 | C2 | semidirect |
| 6. C2×#88104 | C2 | semidirect |
| 7. C2×#88100 | C2 | semidirect |
| 14. C2×C13×SD16 | C4 | semidirect |
| 15. C2×#6107 | C4 | semidirect |
| 16. C2×#6104 | C4 | semidirect |
| 19. C2×#6095 | C4 | semidirect |
| 127. C2×SD16 | #261 | semidirect |
| 183. C13 | #1975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88170 | 2 |
| #11719159 | 2 |
| C2×#88118 | 2 |
| #11719147 | 2 |
| C2×#88116 | 2 |
| C2×#88104 | 2 |
| C2×#88100 | 2 |
| #1975 | 13 |