Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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 |
|---|---|---|
| 4. #11719205 | C2 | direct (N × H) |
| 5. C2×#88144 | C2 | semidirect |
| 6. C2×#88142 | C2 | semidirect |
| 20. #88144 | C22 | semidirect |
| 21. #88142 | C22 | semidirect |
| 24. C22×C4×C13 | Q8 | semidirect |
| 49. C2×C4×C13 | C2×Q8 | semidirect |
| 91. C2×C13 | #544 | semidirect |
| 101. C22×C4 | Dic26 | semidirect |
| 113. C13 | C2×#544 | semidirect |
| 127. C2×C4 | C2×Dic26 | semidirect |
| 143. C2 | #11719205 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×C4⋊C4 | 2 |
| C2×#88180 | 2 |
| C2×#88178 | 2 |
| #11719205 | 2 |
| C2×#88144 | 2 |
| C2×#88142 | 2 |
| C2×#544 | 13 |