Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
644 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 120 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×#5423 | C2 | semidirect |
| 3. C2×C3×GU(2,𝔽3) | C2 | semidirect |
| 4. #85541 | C3 | direct (N × H) |
| 6. C3×2−1+4⋊C3 | C4 | semidirect |
| 7. C3×#994 | C4 | semidirect |
| 10. C3×GU(2,𝔽3) | C22 | semidirect |
| 11. C3×GU(2,𝔽3) | C22 | semidirect |
| 17. #5423 | C2×C3 | semidirect |
| 18. C2×GU(2,𝔽3) | C2×C3 | semidirect |
| 24. C3×#41⋊C3 | C2×C4 | semidirect |
| 26. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 38. 2−1+4⋊C3 | C3×C4 | semidirect |
| 40. #994 | C3×C4 | semidirect |
| 52. GU(2,𝔽3) | C22×C3 | semidirect |
| 53. GU(2,𝔽3) | C22×C3 | semidirect |
| 96. #41⋊C3 | C2×C3×C4 | semidirect |
| 99. C2×SL(2,𝔽3) | C2×C3×C4 | semidirect |
| 266. C3 | #85541 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5945 | 2 |
| C3×#5423 | 2 |
| C2×C3×GU(2,𝔽3) | 2 |
| #85541 | 3 |
| C3×#2901 | 3 |
| C3×#948 | 4 |