Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #11719228 | C2 | semidirect |
| 3. C13×#405 | C2 | semidirect |
| 4. #11718794 | C2 | semidirect |
| 5. C2×#88058 | C2 | semidirect |
| 6. #11718371 | C2 | semidirect |
| 7. C4×Dic52 | C2 | semidirect |
| 8. C4×D104 | C2 | semidirect |
| 15. #88158 | C4 | semidirect |
| 33. #6127 | C2×C4 | semidirect |
| 39. C2×C8×C13 | C2×C4 | semidirect |
| 52. Dic52 | C2×C4 | semidirect |
| 53. D104 | C2×C4 | semidirect |
| 54. #6095 | C2×C4 | semidirect |
| 84. #405 | D13 | semidirect |
| 137. C2×C8 | C4×D13 | semidirect |
| 150. C13 | #2951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| #11719228 | 2 |
| C13×#405 | 2 |
| #11718794 | 2 |
| C2×#88058 | 2 |
| #11718371 | 2 |
| C4×Dic52 | 2 |
| C4×D104 | 2 |
| #2951 | 13 |