Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
774 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 197 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. #10592939 | C2 | semidirect |
| 3. #10589411 | C2 | semidirect |
| 4. #10589407 | C2 | semidirect |
| 6. C2×C32×#41 | C4 | semidirect |
| 8. C32×C4⋊Q8 | C4 | semidirect |
| 10. C32×#124 | C4 | semidirect |
| 14. C2×C32×C42 | C4 | semidirect |
| 47. C2×C3×#41 | Dic3 | semidirect |
| 49. C3×C4⋊Q8 | Dic3 | semidirect |
| 51. C3×#124 | Dic3 | semidirect |
| 55. C2×C3×C42 | Dic3 | semidirect |
| 126. C2×#41 | C3⋊Dic3 | semidirect |
| 128. C4⋊Q8 | C3⋊Dic3 | semidirect |
| 130. #124 | C3⋊Dic3 | semidirect |
| 135. C2×C42 | C3⋊Dic3 | semidirect |
| 206. C32 | #2126 | semidirect |
| 251. C3 | #71819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#532 | 2 |
| #10592939 | 2 |
| #10589411 | 2 |
| #10589407 | 2 |
| #71819 | 3 |