Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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×C13×SD32 | C2 | semidirect |
| 2. #11718852 | C2 | semidirect |
| 3. C2×#88068 | C2 | semidirect |
| 4. #11718812 | C2 | semidirect |
| 5. C2×#88066 | C2 | semidirect |
| 6. C2×D208 | C2 | semidirect |
| 7. #11718094 | C2 | semidirect |
| 42. C13×C16 | D4 | semidirect |
| 43. #6090 | D4 | semidirect |
| 64. C2×SD32 | D13 | semidirect |
| 121. C16 | C22⋊D13 | semidirect |
| 122. C13 | #2250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×SD32 | 2 |
| #11718852 | 2 |
| C2×#88068 | 2 |
| #11718812 | 2 |
| C2×#88066 | 2 |
| C2×D208 | 2 |
| #11718094 | 2 |
| #2250 | 13 |