Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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×#88142 | C2 | semidirect |
| 3. C13×#480 | C2 | semidirect |
| 4. #11718694 | C2 | semidirect |
| 5. #11718628 | C2 | semidirect |
| 6. #11718551 | C2 | semidirect |
| 7. #11718535 | C2 | semidirect |
| 8. #11718421 | C2 | semidirect |
| 9. #11718420 | C2 | semidirect |
| 10. #11718397 | C2 | semidirect |
| 11. #11718379 | C2 | semidirect |
| 119. #480 | D13 | semidirect |
| 217. C13 | #3226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719301 | 2 |
| C2×#88142 | 2 |
| C13×#480 | 2 |
| #11718694 | 2 |
| #11718628 | 2 |
| #11718551 | 2 |
| #11718535 | 2 |
| #11718421 | 2 |
| #11718420 | 2 |
| #11718397 | 2 |
| #11718379 | 2 |
| #3226 | 13 |