Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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×C13×#104 | C2 | semidirect |
| 3. #11718893 | C2 | semidirect |
| 4. #11718794 | C2 | semidirect |
| 5. #11718596 | C2 | semidirect |
| 6. C2×#88045 | C2 | semidirect |
| 7. #11718146 | C2 | semidirect |
| 52. C42×C13 | D4 | semidirect |
| 104. C2×#104 | D13 | semidirect |
| 191. C42 | C22⋊D13 | semidirect |
| 192. C13 | #2039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719538 | 2 |
| C2×C13×#104 | 2 |
| #11718893 | 2 |
| #11718794 | 2 |
| #11718596 | 2 |
| C2×#88045 | 2 |
| #11718146 | 2 |
| #2039 | 13 |