Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
848 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 161 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 | direct (N × H) |
| 5. C2×C3×#41⋊C3 | C4 | semidirect |
| 7. C22×C3×SL(2,𝔽3) | C4 | semidirect |
| 9. C3⋊GU(2,𝔽3) | C22 | direct (N × H) |
| 18. C3×#41⋊C3 | C2×C4 | semidirect |
| 20. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 31. C2×#41⋊C3 | Dic3 | semidirect |
| 33. C22×SL(2,𝔽3) | Dic3 | semidirect |
| 46. C3×SL(2,𝔽3) | C22×C4 | semidirect |
| 75. #41⋊C3 | C2×Dic3 | semidirect |
| 77. C2×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 128. SL(2,𝔽3) | C22×Dic3 | semidirect |
| 165. C22×C3 | GU(2,𝔽3) | semidirect |
| 202. C2×C3 | C2×GU(2,𝔽3) | semidirect |
| 208. C22 | C3⋊GU(2,𝔽3) | direct (N × H) |
| 216. C3 | C22×GU(2,𝔽3) | semidirect |
| 219. C2 | C2×C3⋊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 |
|---|---|
| C22×C3×#41⋊C3 | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| C22×GU(2,𝔽3) | 3 |
| C22×#837 | 3 |
| C22×C3⋊(C3⋊C8) | 4 |