Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
462 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 98 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×#473 | C2 | semidirect |
| 3. C2×C3×#829 | C2 | semidirect |
| 4. C3×#5179 | C2 | semidirect |
| 5. C3×#4561 | C2 | semidirect |
| 6. C3×#4497 | C2 | semidirect |
| 7. C3×#4496 | C2 | semidirect |
| 9. #71099 | C3 | direct (N × H) |
| 32. C3×#473 | D3 | semidirect |
| 33. C3×#473 | C2×C3 | semidirect |
| 34. C2×#829 | C2×C3 | semidirect |
| 35. #5179 | C2×C3 | semidirect |
| 39. #4561 | C2×C3 | semidirect |
| 40. #4497 | C2×C3 | semidirect |
| 41. #4496 | C2×C3 | semidirect |
| 135. #473 | C3×D3 | semidirect |
| 343. C32 | #2195 | semidirect |
| 388. C3 | #71099 | direct (N × H) |
| 389. C3 | C3×#2195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5753 | 2 |
| C32×#473 | 2 |
| C2×C3×#829 | 2 |
| C3×#5179 | 2 |
| C3×#4561 | 2 |
| C3×#4497 | 2 |
| C3×#4496 | 2 |
| C3×#2195 | 3 |
| #71099 | 3 |