Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #11718755 | C2 | semidirect |
| 4. #11718751 | C2 | semidirect |
| 6. #11718692 | C2 | semidirect |
| 7. #11718681 | C2 | semidirect |
| 167. C13 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| #11719175 | 2 |
| #11718755 | 2 |
| #11718751 | 2 |
| #11718713 | 2 |
| #11718692 | 2 |
| #11718681 | 2 |
| #11718585 | 2 |
| #3255 | 13 |