Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
291 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 106 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. #69083 | C3 | direct (N × H) |
| 151. C32 | #2245 | semidirect |
| 173. C3 | #69083 | direct (N × H) |
| 174. C3 | C3×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×#4683 | 2 |
| C32×#346 | 2 |
| C3×#4503 | 2 |
| C3×#2245 | 3 |
| #69083 | 3 |