Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
481 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 481 conjugacy classes of subgroups — too many to draw. Only its 228 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 | direct (N × H) |
| 10. C2×C3×C3⋊C16 | C4 | semidirect |
| 26. C3×C3⋊C16 | C2×C4 | semidirect |
| 40. C2×C3⋊C16 | Dic3 | semidirect |
| 75. C3⋊C16 | C2×Dic3 | semidirect |
| 111. C2×C32 | #346 | semidirect |
| 138. C32 | C2×#346 | semidirect |
| 152. C2×C3 | #4502 | semidirect |
| 163. C3 | C2×#4502 | semidirect |
| 164. C2 | #10589104 | 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 |
| #10589104 | 2 |
| C2×#4502 | 3 |