Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
724 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 141 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. #10593657 | C2 | semidirect |
| 3. C2×C3⋊GU(2,𝔽3) | C2 | semidirect |
| 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 |
| 23. C3×#41⋊C3 | C2×C4 | semidirect |
| 25. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 36. 2−1+4⋊C3 | Dic3 | semidirect |
| 37. #994 | Dic3 | semidirect |
| 89. #41⋊C3 | C2×Dic3 | semidirect |
| 91. C2×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 248. C3 | #85541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5945 | 2 |
| #10593657 | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| #85541 | 3 |
| #84120 | 3 |
| #64157 | 4 |