Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88123 | C2 | semidirect |
| 3. #11718730 | C2 | semidirect |
| 4. #11718721 | C2 | semidirect |
| 5. #11718711 | C2 | semidirect |
| 7. #11718692 | C2 | semidirect |
| 8. #11718680 | C2 | semidirect |
| 9. #11718587 | C2 | semidirect |
| 184. C13 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#529 | 2 |
| C2×#88123 | 2 |
| #11718730 | 2 |
| #11718721 | 2 |
| #11718711 | 2 |
| #11718701 | 2 |
| #11718692 | 2 |
| #11718680 | 2 |
| #11718587 | 2 |
| #3218 | 13 |