Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
659 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 659 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×#5240 | C2 | semidirect |
| 3. C3×#5233 | C2 | semidirect |
| 4. C3×#5119 | C2 | semidirect |
| 5. C3×#4557 | C2 | semidirect |
| 7. #72115 | C3 | direct (N × H) |
| 26. #5240 | C2×C3 | semidirect |
| 27. #5233 | C2×C3 | semidirect |
| 28. #5119 | C2×C3 | semidirect |
| 30. #4557 | C2×C3 | semidirect |
| 299. C32 | #2053 | semidirect |
| 343. C3 | #72115 | direct (N × H) |
| 344. C3 | C3×#2053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#575 | 2 |
| C3×#5240 | 2 |
| C3×#5233 | 2 |
| C3×#5119 | 2 |
| C3×#4557 | 2 |
| C3×#2053 | 3 |
| #72115 | 3 |