Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88144 | C2 | semidirect |
| 3. C2×C13×#102 | C2 | semidirect |
| 4. C2×#88072 | C2 | semidirect |
| 5. C2×#88061 | C2 | semidirect |
| 6. C2×#88055 | C2 | semidirect |
| 7. C2×#88049 | C2 | semidirect |
| 8. #11718425 | C2 | direct (N × H) |
| 23. #88144 | C22 | semidirect |
| 24. C13×#102 | C22 | semidirect |
| 25. #88072 | C22 | semidirect |
| 26. #88061 | C22 | semidirect |
| 27. #88055 | C22 | semidirect |
| 28. #88049 | C22 | semidirect |
| 98. C2×#102 | D13 | semidirect |
| 137. #102 | C2×D13 | semidirect |
| 140. C2×C13 | #490 | semidirect |
| 176. C13 | C2×#490 | semidirect |
| 229. C2 | #11718425 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88194 | 2 |
| C2×#88144 | 2 |
| C2×C13×#102 | 2 |
| C2×#88072 | 2 |
| C2×#88061 | 2 |
| C2×#88055 | 2 |
| C2×#88049 | 2 |
| #11718425 | 2 |
| C2×#490 | 13 |