Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×C4⋊#1055 | C2 | semidirect |
| 5. #11718116 | C2 | semidirect |
| 28. C13×C22⋊C4 | C8 | semidirect |
| 56. C2×C4×C13 | C2×C8 | semidirect |
| 73. C22×C13 | C4⋊C8 | semidirect |
| 121. C22⋊C4 | #1055 | semidirect |
| 124. C13 | #1850 | semidirect |
| 140. C2×C4 | C2×#1055 | semidirect |
| 153. C22 | C4⋊#1055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1055 | 2 |
| C4×C13×C22⋊C4 | 2 |
| C2×C22⋊#1055 | 2 |
| C2×C4⋊#1055 | 2 |
| #11718116 | 2 |
| #1850 | 13 |