Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
397 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 397 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 7. #68924 | C3 | direct (N × H) |
| 198. C32 | #2090 | semidirect |
| 228. C3 | #68924 | direct (N × H) |
| 229. C3 | C3×#2090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5121 | 2 |
| C2×C3×#817 | 2 |
| C3×#5102 | 2 |
| C32×#341 | 2 |
| C3×#4554 | 2 |
| C3×#2090 | 3 |
| #68924 | 3 |