Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88205 | C2 | semidirect |
| 3. C2×#88155 | C2 | semidirect |
| 4. #11719231 | C2 | semidirect |
| 5. C13×#416 | C2 | semidirect |
| 6. C2×#88056 | C2 | semidirect |
| 7. #11718656 | C2 | semidirect |
| 8. #11718477 | C2 | semidirect |
| 9. #11718474 | C2 | semidirect |
| 10. #11718441 | C2 | semidirect |
| 11. #11718439 | C2 | semidirect |
| 81. #6099 | D4 | semidirect |
| 128. #416 | D13 | semidirect |
| 228. C13 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719538 | 2 |
| C2×#88205 | 2 |
| C2×#88155 | 2 |
| #11719231 | 2 |
| C13×#416 | 2 |
| C2×#88056 | 2 |
| #11718656 | 2 |
| #11718477 | 2 |
| #11718474 | 2 |
| #11718441 | 2 |
| #11718439 | 2 |
| #3063 | 13 |