Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
529 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 529 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊(#131⋊C3) | C2 | semidirect |
| 3. C2×C3⋊GU(2,𝔽3) | C2 | semidirect |
| 4. #10593221 | C2 | direct (N × H) |
| 8. C3×#985 | C4 | semidirect |
| 10. C2×C3×GL(2,𝔽3) | C4 | semidirect |
| 11. C2×C3×#226 | C4 | semidirect |
| 13. C3⋊(#131⋊C3) | C22 | semidirect |
| 14. C3⋊GU(2,𝔽3) | C22 | semidirect |
| 18. C2×#948 | D3 | semidirect |
| 33. C3×GL(2,𝔽3) | C2×C4 | semidirect |
| 34. C3×#226 | C2×C4 | semidirect |
| 43. #985 | Dic3 | semidirect |
| 45. C2×GL(2,𝔽3) | Dic3 | semidirect |
| 46. C2×#226 | Dic3 | semidirect |
| 59. #948 | C2×D3 | semidirect |
| 115. GL(2,𝔽3) | C2×Dic3 | semidirect |
| 116. #226 | C2×Dic3 | semidirect |
| 320. C2×C3 | #5405 | semidirect |
| 337. C3 | C2×#5405 | semidirect |
| 341. C2 | #10593221 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#985 | 2 |
| C2×C3⋊(#131⋊C3) | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| #10593221 | 2 |
| C2×#5405 | 3 |
| C2×#5197 | 3 |
| C2×#3711 | 4 |