Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
755 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 755 conjugacy classes of subgroups — too many to draw. Only its 111 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×#519⋊C3 | C2 | semidirect |
| 3. #5812⋊C3 | C2 | semidirect |
| 4. #5574⋊C3 | C2 | semidirect |
| 5. C4×C3⋊(#41⋊C3) | C2 | semidirect |
| 6. #85872 | C3 | semidirect |
| 9. C2×C3⋊(#41⋊C3) | C4 | semidirect |
| 13. C3×C4×SL(2,𝔽3) | C22 | semidirect |
| 14. Dic3×SL(2,𝔽3) | C22 | semidirect |
| 20. #5574 | C2×C3 | semidirect |
| 22. C4×#239 | C2×C3 | semidirect |
| 30. #519⋊C3 | D3 | semidirect |
| 33. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 35. C3⋊(#41⋊C3) | C2×C4 | semidirect |
| 36. C3⋊(#41⋊C3) | C2×C4 | semidirect |
| 46. C2×#239 | C3×C4 | semidirect |
| 86. C4×SL(2,𝔽3) | C2×D3 | semidirect |
| 139. C2×SL(2,𝔽3) | C4×D3 | semidirect |
| 396. C3 | #3428⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(#41⋊C3) | 2 |
| C3×#519⋊C3 | 2 |
| #5812⋊C3 | 2 |
| #5574⋊C3 | 2 |
| C4×C3⋊(#41⋊C3) | 2 |
| #85872 | 3 |
| #3428⋊C3 | 3 |
| C3×#877 | 4 |