Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. C13×#462 | C2 | semidirect |
| 5. #11718845 | C2 | semidirect |
| 6. #11718751 | C2 | semidirect |
| 7. #11718681 | C2 | semidirect |
| 8. #11718512 | C2 | semidirect |
| 11. #11718450 | C2 | semidirect |
| 118. #462 | D13 | semidirect |
| 214. C13 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| C4×Q8×D13 | 2 |
| C13×#462 | 2 |
| #11718847 | 2 |
| #11718845 | 2 |
| #11718751 | 2 |
| #11718681 | 2 |
| #11718512 | 2 |
| #11718496 | 2 |
| #11718466 | 2 |
| #11718450 | 2 |
| #3113 | 13 |