Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
449 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 449 conjugacy classes of subgroups — too many to draw. Only its 196 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. #10589133 | C2 | direct (N × H) |
| 50. C2×C3⋊Dic3 | C16 | semidirect |
| 92. C3⋊Dic3 | C2×C16 | semidirect |
| 126. C2×C32 | C4⋊C16 | semidirect |
| 160. C32 | C2×C4⋊C16 | semidirect |
| 178. C2×C3 | Dic3⋊C16 | semidirect |
| 192. C3 | C2×Dic3⋊C16 | semidirect |
| 193. C2 | #10589133 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊Dic3 | 2 |
| C22×C3×C3⋊C16 | 2 |
| #10589133 | 2 |
| C2×Dic3⋊C16 | 3 |