Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 8. #11718458 | C2 | semidirect |
| 9. #11718453 | C2 | semidirect |
| 162. C13 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88198 | 2 |
| #11719222 | 2 |
| C13×#419 | 2 |
| #11718886 | 2 |
| #11718781 | 2 |
| M16×Dic13 | 2 |
| #11718665 | 2 |
| #11718458 | 2 |
| #11718453 | 2 |
| #3139 | 13 |