Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 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. C13×#428 | C2 | semidirect |
| 3. C2×#88065 | C2 | semidirect |
| 4. C2×#88063 | C2 | semidirect |
| 5. #11718649 | C2 | semidirect |
| 6. #11718627 | C2 | semidirect |
| 7. #11718124 | C2 | semidirect |
| 48. C13×M16 | D4 | semidirect |
| 103. #428 | D13 | semidirect |
| 180. M16 | D52 | semidirect |
| 194. C13 | #2037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719230 | 2 |
| C13×#428 | 2 |
| C2×#88065 | 2 |
| C2×#88063 | 2 |
| #11718649 | 2 |
| #11718627 | 2 |
| #11718124 | 2 |
| #2037 | 13 |