Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 2. C23×#1055 | C2 | semidirect |
| 3. C2×C22⋊#1055 | C2 | semidirect |
| 4. C2×C22⋊#1055 | C2 | semidirect |
| 5. #11718116 | C2 | semidirect |
| 25. C2×D4×C13 | C8 | semidirect |
| 50. C2×#1055 | D4 | semidirect |
| 60. C23×C13 | C2×C8 | semidirect |
| 78. C2×C4×C13 | C2×C8 | semidirect |
| 99. C22×C13 | C22⋊C8 | semidirect |
| 138. C2×D4 | #1055 | semidirect |
| 164. C13 | #1869 | semidirect |
| 172. C23 | C2×#1055 | semidirect |
| 190. C2×C4 | C2×#1055 | semidirect |
| 207. C22 | C22⋊#1055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C23×#1055 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718116 | 2 |
| #1869 | 13 |