Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11718843 | C2 | semidirect |
| 7. #11718515 | C2 | semidirect |
| 8. #11718454 | C2 | semidirect |
| 9. #11718452 | C2 | semidirect |
| 163. C13 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719327 | 2 |
| C13×#470 | 2 |
| #11718843 | 2 |
| #11718798 | 2 |
| #11718779 | 2 |
| #11718713 | 2 |
| #11718515 | 2 |
| #11718454 | 2 |
| #11718452 | 2 |
| #3255 | 13 |