Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1829 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1829 conjugacy classes of subgroups — too many to draw. Only its 198 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 |
|---|---|---|
| 1. C22×C32×H(3,𝔽3) | C2 | semidirect |
| 2. C2×C3×C3⋊#272 | C2 | semidirect |
| 3. C3×C3⋊#1084 | C2 | semidirect |
| 5. #10619994 | C3 | direct (N × H) |
| 10. C22×C34 | D3 | semidirect |
| 15. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 16. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 17. C2×C3⋊#272 | C2×C3 | semidirect |
| 19. C3⋊#1084 | C2×C3 | semidirect |
| 21. C32×H(3,𝔽3) | D4 | semidirect |
| 44. C22×C33 | C3×D3 | semidirect |
| 46. C22×C33 | C3⋊D3 | semidirect |
| 56. C22×H(3,𝔽3) | C3×D3 | semidirect |
| 59. C34 | #67 | semidirect |
| 62. C3×H(3,𝔽3) | #67 | semidirect |
| 63. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 103. C22×C32 | #272 | semidirect |
| 105. C22×C32 | C3×C3⋊D3 | semidirect |
| 122. C33 | C3×#67 | semidirect |
| 124. C33 | #638 | semidirect |
| 126. H(3,𝔽3) | C3×#67 | semidirect |
| 169. C22×C3 | C3×#272 | semidirect |
| 170. C22×C3 | C3⋊#272 | semidirect |
| 187. C32 | #6235 | semidirect |
| 189. C32 | C3×#638 | semidirect |
| 211. C22 | C3×C3⋊#272 | semidirect |
| 217. C3 | C3×#6235 | semidirect |
| 218. C3 | #10619994 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×H(3,𝔽3) | 2 |
| C2×C3×C3⋊#272 | 2 |
| C3×C3⋊#1084 | 2 |
| C32×#638 | 3 |
| #10619994 | 3 |
| C3×#6235 | 3 |