Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 6. #11718594 | C2 | semidirect |
| 7. #11718594 | C2 | semidirect |
| 8. #11718321 | C2 | semidirect |
| 9. #11718318 | C2 | semidirect |
| 162. C13 | #2569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×C22⋊C4 | 2 |
| #11718873 | 2 |
| C2×#88071 | 2 |
| #11718607 | 2 |
| #11718603 | 2 |
| #11718594 | 2 |
| #11718321 | 2 |
| #11718318 | 2 |
| #2569 | 13 |