Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 6. #71310 | C3 | direct (N × H) |
| 181. C32 | #2241 | semidirect |
| 209. C3 | #71310 | direct (N × H) |
| 210. C3 | C3×#2241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C3×#4682 | 2 |
| C3×#4564 | 2 |
| C3×C4×C3⋊C16 | 2 |
| C3×#2241 | 3 |
| #71310 | 3 |