Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#88106 | C2 | semidirect |
| 3. C2×#88106 | C2 | semidirect |
| 4. #11718270 | C2 | semidirect |
| 17. #88106 | C22 | semidirect |
| 19. C2×#6092 | C22 | semidirect |
| 126. C13 | #2117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88161 | 2 |
| C2×#88106 | 2 |
| #11718270 | 2 |
| #2117 | 13 |