Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
737 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 737 conjugacy classes of subgroups — too many to draw. Only its 91 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⋊GU(2,𝔽3) | C2 | semidirect |
| 3. C2×C3×GU(2,𝔽3) | C2 | semidirect |
| 4. D3×GU(2,𝔽3) | C2 | direct (N × H) |
| 8. D3×#41⋊C3 | C4 | semidirect |
| 10. C2×D3×SL(2,𝔽3) | C4 | semidirect |
| 11. C2×C3⋊(#41⋊C3) | C4 | semidirect |
| 13. C3⋊GU(2,𝔽3) | C22 | semidirect |
| 14. C3×GU(2,𝔽3) | C22 | semidirect |
| 22. C2×GU(2,𝔽3) | D3 | direct (N × H) |
| 30. C3×#41⋊C3 | C2×C4 | semidirect |
| 32. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 33. D3×SL(2,𝔽3) | C2×C4 | semidirect |
| 34. C3⋊(#41⋊C3) | C2×C4 | semidirect |
| 71. GU(2,𝔽3) | C2×D3 | direct (N × H) |
| 83. C3×SL(2,𝔽3) | C22×C4 | semidirect |
| 137. #41⋊C3 | C4×D3 | semidirect |
| 141. C2×SL(2,𝔽3) | C4×D3 | semidirect |
| 241. SL(2,𝔽3) | C2×C4×D3 | semidirect |
| 313. C2×D3 | GU(2,𝔽3) | direct (N × H) |
| 378. C2×C3 | C2×GU(2,𝔽3) | semidirect |
| 381. D3 | C2×GU(2,𝔽3) | direct (N × H) |
| 402. C3 | C22×GU(2,𝔽3) | semidirect |
| 407. C2 | D3×GU(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#41⋊C3 | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| C2×C3×GU(2,𝔽3) | 2 |
| D3×GU(2,𝔽3) | 2 |
| C22×GU(2,𝔽3) | 3 |
| C2×D3×#104 | 3 |
| C2×D3×C3⋊C8 | 4 |