Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
761 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 761 conjugacy classes of subgroups — too many to draw. Only its 140 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) |
| 3. C22×GU(2,𝔽3) | C3 | 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) |
| 15. C2×GU(2,𝔽3) | C2×C3 | direct (N × H) |
| 19. C3×#41⋊C3 | C2×C4 | semidirect |
| 21. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 34. C2×#41⋊C3 | C3×C4 | semidirect |
| 37. C22×SL(2,𝔽3) | C3×C4 | semidirect |
| 44. GU(2,𝔽3) | C22×C3 | direct (N × H) |
| 50. C3×SL(2,𝔽3) | C22×C4 | semidirect |
| 82. #41⋊C3 | C2×C3×C4 | semidirect |
| 85. C2×SL(2,𝔽3) | C2×C3×C4 | semidirect |
| 140. SL(2,𝔽3) | C22×C3×C4 | semidirect |
| 179. C22×C3 | GU(2,𝔽3) | direct (N × H) |
| 220. C2×C3 | C2×GU(2,𝔽3) | direct (N × H) |
| 226. C22 | C3×GU(2,𝔽3) | direct (N × H) |
| 235. C3 | C22×GU(2,𝔽3) | direct (N × H) |
| 238. 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×C3×#104 | 3 |
| C22×C3×C3⋊C8 | 4 |