Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. C2×C4⋊C4×D13 | C2 | semidirect |
| 3. C2×C13×#107 | C2 | semidirect |
| 4. C2×#88061 | C2 | semidirect |
| 5. C2×#88060 | C2 | semidirect |
| 6. C2×#88049 | C2 | semidirect |
| 7. C2×#88047 | C2 | semidirect |
| 8. #11718543 | C2 | direct (N × H) |
| 23. C4⋊C4×D13 | C22 | semidirect |
| 24. C13×#107 | C22 | semidirect |
| 25. #88061 | C22 | semidirect |
| 26. #88060 | C22 | semidirect |
| 27. #88049 | C22 | semidirect |
| 28. #88047 | C22 | semidirect |
| 96. C2×#107 | D13 | semidirect |
| 135. #107 | C2×D13 | semidirect |
| 139. C2×C13 | #480 | semidirect |
| 176. C13 | C2×#480 | semidirect |
| 229. C2 | #11718543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88149 | 2 |
| C2×C4⋊C4×D13 | 2 |
| C2×C13×#107 | 2 |
| C2×#88061 | 2 |
| C2×#88060 | 2 |
| C2×#88049 | 2 |
| C2×#88047 | 2 |
| #11718543 | 2 |
| C2×#480 | 13 |