Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. C2×#88067 | C2 | semidirect |
| 3. #11718777 | C2 | semidirect |
| 4. C22×#6090 | C2 | semidirect |
| 5. #11718154 | C2 | semidirect |
| 6. #11718084 | C2 | semidirect |
| 7. #11718082 | C2 | semidirect |
| 39. #6090 | D4 | semidirect |
| 70. C22×C13 | SD32 | semidirect |
| 115. C13 | #2217 | semidirect |
| 138. C22 | #88067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#466 | 2 |
| C2×#88067 | 2 |
| #11718777 | 2 |
| C22×#6090 | 2 |
| #11718154 | 2 |
| #11718084 | 2 |
| #11718082 | 2 |
| #2217 | 13 |