Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
367 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 367 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 |
|---|---|---|
| 2. C2×C3×#818 | C2 | semidirect |
| 3. C3×#4562 | C2 | semidirect |
| 4. C3×#4549 | C2 | semidirect |
| 5. C3×#4490 | C2 | semidirect |
| 7. #71069 | C3 | direct (N × H) |
| 21. C2×#818 | C2×C3 | semidirect |
| 25. #4562 | C2×C3 | semidirect |
| 26. #4549 | C2×C3 | semidirect |
| 27. #4490 | C2×C3 | semidirect |
| 233. C32 | #2233 | semidirect |
| 276. C3 | #71069 | direct (N × H) |
| 277. C3 | C3×#2233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#466 | 2 |
| C2×C3×#818 | 2 |
| C3×#4562 | 2 |
| C3×#4549 | 2 |
| C3×#4490 | 2 |
| C3×#2233 | 3 |
| #71069 | 3 |