Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
596 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 153 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×#6101 | C2 | semidirect |
| 3. C4×C13×C22⋊C4 | C2 | semidirect |
| 4. #11718619 | C2 | semidirect |
| 5. #11718619 | C2 | semidirect |
| 6. #11718601 | C2 | semidirect |
| 7. #11718333 | C2 | semidirect |
| 8. #11718320 | C2 | semidirect |
| 89. C4×C22⋊C4 | D13 | semidirect |
| 158. C13 | #2591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88184 | 2 |
| C22×#6101 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718619 | 2 |
| #11718601 | 2 |
| #11718333 | 2 |
| #11718320 | 2 |
| #2591 | 13 |