Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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. #11719385 | C2 | semidirect |
| 2. C13×#495 | C2 | semidirect |
| 3. #11718850 | C2 | semidirect |
| 4. #11718845 | C2 | semidirect |
| 5. #11718835 | C2 | semidirect |
| 6. #11718825 | C2 | semidirect |
| 8. #11718813 | C2 | semidirect |
| 9. #11718717 | C2 | semidirect |
| 10. C4×#6094 | C2 | semidirect |
| 11. #11718344 | C2 | semidirect |
| 94. #495 | D13 | semidirect |
| 178. C13 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719385 | 2 |
| C13×#495 | 2 |
| #11718850 | 2 |
| #11718845 | 2 |
| #11718835 | 2 |
| #11718825 | 2 |
| #11718820 | 2 |
| #11718813 | 2 |
| #11718717 | 2 |
| C4×#6094 | 2 |
| #11718344 | 2 |
| #3183 | 13 |