Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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×#64214 | C2 | semidirect |
| 3. C2×#64213 | C2 | semidirect |
| 4. #10593269 | C2 | direct (N × H) |
| 17. #64214 | C22 | semidirect |
| 19. #64213 | C22 | semidirect |
| 125. C2×C32 | #350 | semidirect |
| 164. C32 | C2×#350 | semidirect |
| 207. C2 | #10593269 | 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×#64214 | 2 |
| C2×#64213 | 2 |
| #10593269 | 2 |
| C2×#350 | 9 |