Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1068 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 203 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. #11758013 | C2 | direct (N × H) |
| 3. C2×C3×#1084 | C3 | semidirect |
| 5. C2×H(5,𝔽3) | C4 | semidirect |
| 10. C3×#1084 | C2×C3 | semidirect |
| 12. H(5,𝔽3) | C2×C4 | semidirect |
| 15. C2×#1084 | C32 | semidirect |
| 18. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 19. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 31. #1084 | C2×C32 | semidirect |
| 33. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 34. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 40. C2×C33 | C3×Dic3 | semidirect |
| 61. C33 | C2×C3×Dic3 | semidirect |
| 107. C2 | #11758013 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×H(5,𝔽3) | 2 |
| #11758013 | 2 |
| C2×C3×#1084 | 3 |
| C2×Dic3×H(3,𝔽3) | 3 |