Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#88123 | C2 | semidirect |
| 5. C2×#88064 | C2 | semidirect |
| 6. #11718781 | C2 | semidirect |
| 7. #11718115 | C2 | semidirect |
| 194. C13 | #2005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719530 | 2 |
| C2×#88205 | 2 |
| C2×#88123 | 2 |
| C2×C13×#104 | 2 |
| C2×#88064 | 2 |
| #11718781 | 2 |
| #11718115 | 2 |
| #2005 | 13 |