Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×C13×D8 | C2 | semidirect |
| 2. #11719510 | C2 | semidirect |
| 3. C2×#88186 | C2 | semidirect |
| 4. C2×#88158 | C2 | semidirect |
| 5. #11718816 | C2 | semidirect |
| 6. #11718815 | C2 | semidirect |
| 7. #11718812 | C2 | semidirect |
| 8. #11718762 | C2 | semidirect |
| 16. #88194 | C22 | semidirect |
| 18. #88190 | C22 | semidirect |
| 19. C2×#6105 | C22 | semidirect |
| 21. C2×#6104 | C22 | semidirect |
| 24. C2×Dic52 | C22 | semidirect |
| 26. C2×D104 | C22 | semidirect |
| 27. C2×#6095 | C22 | semidirect |
| 28. #88055 | C22 | semidirect |
| 29. C8×Dic13 | C22 | semidirect |
| 45. C2×C8×C13 | D4 | semidirect |
| 54. #6099 | D4 | semidirect |
| 86. C22×D8 | D13 | semidirect |
| 153. C2×C8 | C22⋊D13 | semidirect |
| 160. C13 | #3155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×D8 | 2 |
| #11719510 | 2 |
| C2×#88186 | 2 |
| C2×#88158 | 2 |
| #11718816 | 2 |
| #11718815 | 2 |
| #11718812 | 2 |
| #11718762 | 2 |
| #3155 | 13 |