Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88050 | C2 | semidirect |
| 5. #11718590 | C2 | semidirect |
| 6. C2×C4⋊#1055 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 80. C2×C4×C13 | SD16 | semidirect |
| 188. C13 | #2055 | semidirect |
| 219. C2×C4 | #6105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6105 | 2 |
| C13×#390 | 2 |
| C2×#88072 | 2 |
| C2×#88050 | 2 |
| #11718590 | 2 |
| C2×C4⋊#1055 | 2 |
| #11718121 | 2 |
| #2055 | 13 |