Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #11719421 | C2 | semidirect |
| 2. #11719421 | C2 | semidirect |
| 3. C13×#493 | C2 | semidirect |
| 4. #11718819 | C2 | semidirect |
| 5. #11718814 | C2 | semidirect |
| 6. #11718737 | C2 | semidirect |
| 7. #11718731 | C2 | semidirect |
| 8. #11718346 | C2 | semidirect |
| 9. #11718342 | C2 | semidirect |
| 99. #493 | D13 | semidirect |
| 188. C13 | #3207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| C13×#493 | 2 |
| #11718819 | 2 |
| #11718814 | 2 |
| #11718737 | 2 |
| #11718731 | 2 |
| #11718346 | 2 |
| #11718342 | 2 |
| #3207 | 13 |