Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C2×#88163 | C2 | semidirect |
| 3. C22×#6095 | C2 | semidirect |
| 4. C2×#88064 | C2 | semidirect |
| 5. C2×#88063 | C2 | semidirect |
| 6. #11718771 | C2 | semidirect |
| 7. C13×#341 | C2 | semidirect |
| 112. #341 | D13 | semidirect |
| 196. C13 | #2019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88163 | 2 |
| C2×#88162 | 2 |
| C22×#6095 | 2 |
| C2×#88064 | 2 |
| C2×#88063 | 2 |
| #11718771 | 2 |
| C13×#341 | 2 |
| #2019 | 13 |