Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 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×#88237 | C2 | semidirect |
| 3. C2×#88119 | C2 | semidirect |
| 4. #11719142 | C2 | direct (N × H) |
| 5. C22×D4×C13 | C4 | semidirect |
| 7. C23×Dic13 | C4 | semidirect |
| 11. C2×#6129 | C4 | semidirect |
| 14. C22×Dic26 | C4 | semidirect |
| 17. #88237 | C22 | semidirect |
| 20. #88119 | C22 | semidirect |
| 26. C2×D4×C13 | C2×C4 | semidirect |
| 37. C22×Dic13 | C2×C4 | semidirect |
| 49. C2×Dic26 | C2×C4 | semidirect |
| 117. C22×D4 | #261 | semidirect |
| 129. C2×C13 | #410 | semidirect |
| 148. C2×D4 | C2×#261 | semidirect |
| 166. C13 | C2×#410 | semidirect |
| 223. C2 | #11719142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6129 | 2 |
| C2×#88237 | 2 |
| C2×#88119 | 2 |
| #11719142 | 2 |
| C2×#410 | 13 |