Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
595 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 595 conjugacy classes of subgroups — too many to draw. Only its 130 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. C32×#423 | C2 | semidirect |
| 3. C3×#5132 | C2 | semidirect |
| 4. C2×C3×#805 | C2 | semidirect |
| 5. C3×C3⋊#338 | C2 | semidirect |
| 7. #70531 | C3 | direct (N × H) |
| 24. C3×#423 | D3 | semidirect |
| 25. C3×#423 | C2×C3 | semidirect |
| 28. #5132 | C2×C3 | semidirect |
| 29. C2×#805 | C2×C3 | semidirect |
| 31. C3⋊#338 | C2×C3 | semidirect |
| 108. #423 | C3×D3 | semidirect |
| 300. C32 | #2050 | semidirect |
| 345. C3 | #70531 | direct (N × H) |
| 346. C3 | C3×#2050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C32×#423 | 2 |
| C3×#5132 | 2 |
| C2×C3×#805 | 2 |
| C3×C3⋊#338 | 2 |
| C3×#2050 | 3 |
| #70531 | 3 |