Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 191 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×#64218 | C2 | semidirect |
| 3. C22×#3771 | C2 | semidirect |
| 4. #10596485 | C2 | direct (N × H) |
| 5. C2×#64214 | C2 | semidirect |
| 6. C2×#64213 | C2 | semidirect |
| 14. #64218 | C22 | semidirect |
| 18. C2×#3771 | C22 | semidirect |
| 19. #64214 | C22 | semidirect |
| 20. #64213 | C22 | semidirect |
| 107. C2×C32 | #504 | semidirect |
| 138. C32 | C2×#504 | semidirect |
| 171. C2 | #10596485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64287 | 2 |
| C2×#64218 | 2 |
| C22×#3771 | 2 |
| #10596485 | 2 |
| C2×#64214 | 2 |
| C2×#64213 | 2 |
| C2×#504 | 9 |