Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
337 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 148 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. #10589144 | C2 | direct (N × H) |
| 121. C2×C32 | #368 | semidirect |
| 150. C32 | C2×#368 | semidirect |
| 169. C2×C3 | #4493 | semidirect |
| 180. C3 | C2×#4493 | semidirect |
| 183. C2 | #10589144 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C16) | 2 |
| C2×C3×#819 | 2 |
| #10589144 | 2 |
| C2×#4493 | 3 |