Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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. #11719209 | C2 | semidirect |
| 3. C2×C13×#106 | C2 | semidirect |
| 4. #11718762 | C2 | semidirect |
| 5. #11718627 | C2 | semidirect |
| 6. #11718530 | C2 | semidirect |
| 7. #11718514 | C2 | semidirect |
| 8. #11718513 | C2 | semidirect |
| 16. #88158 | C4 | semidirect |
| 33. #6127 | C2×C4 | semidirect |
| 38. C2×C8×C13 | C2×C4 | semidirect |
| 51. Dic52 | C2×C4 | semidirect |
| 52. D104 | C2×C4 | semidirect |
| 53. #6095 | C2×C4 | semidirect |
| 80. C2×#106 | D13 | semidirect |
| 133. C2×C8 | C4×D13 | semidirect |
| 144. C13 | #2952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| #11719209 | 2 |
| C2×C13×#106 | 2 |
| #11718762 | 2 |
| #11718627 | 2 |
| #11718530 | 2 |
| #11718514 | 2 |
| #11718513 | 2 |
| #2952 | 13 |