Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 200 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. #10589104 | C2 | semidirect |
| 4. #10589102 | C2 | semidirect |
| 13. C3×#812 | C4 | semidirect |
| 32. C3×C3⋊C16 | C2×C4 | semidirect |
| 50. #812 | Dic3 | semidirect |
| 92. C3⋊C16 | C2×Dic3 | semidirect |
| 100. C3⋊Dic3 | M32 | semidirect |
| 166. C32 | C4×M32 | semidirect |
| 194. C3 | Dic3×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊Dic3 | 2 |
| C2×C3×#812 | 2 |
| #10589104 | 2 |
| #10589102 | 2 |
| Dic3×M32 | 3 |