Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
645 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 645 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10593228 | 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 | semidirect |
| 33. D3×SL(2,𝔽3) | C2×C4 | semidirect |
| 34. C3⋊(#41⋊C3) | C2×C4 | semidirect |
| 71. GU(2,𝔽3) | C2×D3 | semidirect |
| 374. C2×C3 | #5423 | semidirect |
| 398. C3 | C2×#5423 | semidirect |
| 403. C2 | #10593228 | 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 |
| #10593228 | 2 |
| C2×#5423 | 3 |
| C2×#4821 | 3 |
| C2×#3711 | 4 |