Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
196 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. #11718231 | C2 | semidirect |
| 4. C4×#6092 | C2 | semidirect |
| 8. #88106 | C4 | direct (N × H) |
| 25. #6092 | C2×C4 | semidirect |
| 48. C4×C13 | M32 | semidirect |
| 75. C13 | C4×M32 | semidirect |
| 92. C4 | #88106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88106 | 2 |
| C2×C4×#1055 | 2 |
| #11718231 | 2 |
| C4×#6092 | 2 |
| C4×M32 | 13 |