Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#6118 | C2 | semidirect |
| 3. C22×D13⋊C8 | C2 | semidirect |
| 4. C2×C22⋊#1057 | C2 | semidirect |
| 5. #11719147 | C2 | direct (N × H) |
| 18. C2×#6118 | C22 | semidirect |
| 20. C2×D13⋊C8 | C22 | semidirect |
| 21. C22⋊#1057 | C22 | semidirect |
| 113. C2×C13 | #408 | semidirect |
| 145. C13 | C2×#408 | semidirect |
| 188. C2 | #11719147 | 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 |
| C22×#6118 | 2 |
| C22×D13⋊C8 | 2 |
| C2×C22⋊#1057 | 2 |
| #11719147 | 2 |
| C2×#408 | 13 |