Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
663 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 663 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 2. C3×#5237 | C2 | semidirect |
| 3. C2×C3×#837 | C2 | semidirect |
| 4. C3×#5118 | C2 | semidirect |
| 5. C3×C3⋊#338 | C2 | semidirect |
| 7. #72117 | C3 | direct (N × H) |
| 27. #5237 | C2×C3 | semidirect |
| 28. C2×#837 | C2×C3 | semidirect |
| 29. #5118 | C2×C3 | semidirect |
| 31. C3⋊#338 | C2×C3 | semidirect |
| 313. C32 | #2050 | semidirect |
| 359. C3 | #72117 | direct (N × H) |
| 360. C3 | C3×#2050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#575 | 2 |
| C3×#5237 | 2 |
| C2×C3×#837 | 2 |
| C3×#5118 | 2 |
| C3×C3⋊#338 | 2 |
| C3×#2050 | 3 |
| #72117 | 3 |