Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
605 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 50 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. C3×C3⋊#1088 | C2 | direct (N × H) |
| 3. C2×C3⋊#1088 | C3 | direct (N × H) |
| 5. C2×C32×H(3,𝔽3) | C4 | semidirect |
| 6. C32×#272 | C4 | semidirect |
| 12. C3⋊#1088 | C2×C3 | direct (N × H) |
| 14. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 24. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 25. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 28. C3×#272 | Dic3 | semidirect |
| 29. C3×#272 | C3×C4 | semidirect |
| 46. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 47. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 77. C2×H(3,𝔽3) | C3×Dic3 | semidirect |
| 78. #272 | C3×Dic3 | semidirect |
| 107. H(3,𝔽3) | C2×C3×Dic3 | semidirect |
| 135. C2×C32 | #1088 | semidirect |
| 171. C32 | C2×#1088 | semidirect |
| 191. C2×C3 | C3×#1088 | semidirect |
| 192. C2×C3 | C3⋊#1088 | direct (N × H) |
| 204. C3 | C2×C3×#1088 | semidirect |
| 205. C3 | C2×C3⋊#1088 | direct (N × H) |
| 209. C2 | C3×C3⋊#1088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#272 | 2 |
| C3×C3⋊#1088 | 2 |
| C2×C3⋊#1088 | 3 |
| C2×C3×#1088 | 3 |
| C2×C32×Dic3 | 9 |