Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 309 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. #69065 | C3 | direct (N × H) |
| 171. C32 | #2241 | semidirect |
| 199. C3 | #69065 | direct (N × H) |
| 200. C3 | C3×#2241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×#4682 | 2 |
| C32×C4×C16 | 2 |
| C3×#4503 | 2 |
| C3×#2241 | 3 |
| #69065 | 3 |