Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11719262 | C2 | semidirect |
| 3. C13×#459 | C2 | semidirect |
| 4. #11718819 | C2 | semidirect |
| 5. #11718816 | C2 | semidirect |
| 6. #11718736 | C2 | semidirect |
| 7. #11718680 | C2 | semidirect |
| 8. #11718510 | C2 | semidirect |
| 9. #11718494 | C2 | semidirect |
| 10. #11718444 | C2 | semidirect |
| 11. #11718429 | C2 | semidirect |
| 125. #459 | D13 | semidirect |
| 228. C13 | #3212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| #11719262 | 2 |
| C13×#459 | 2 |
| #11718819 | 2 |
| #11718816 | 2 |
| #11718736 | 2 |
| #11718680 | 2 |
| #11718510 | 2 |
| #11718494 | 2 |
| #11718444 | 2 |
| #11718429 | 2 |
| #3212 | 13 |