Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1928 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 1928 conjugacy classes of subgroups — too many to draw. Only its 192 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×C32×#272 | C2 | semidirect |
| 3. C32×#1084 | C2 | semidirect |
| 5. C3×#6235 | C3 | direct (N × H) |
| 9. C22×C34 | D3 | semidirect |
| 13. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C2×C3×#272 | C2×C3 | semidirect |
| 15. C3×#1084 | C2×C3 | semidirect |
| 16. C32×H(3,𝔽3) | D4 | semidirect |
| 20. #6235 | C32 | direct (N × H) |
| 32. C22×C33 | C3×D3 | semidirect |
| 41. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 42. C2×#272 | C2×C32 | semidirect |
| 43. #1084 | C2×C32 | semidirect |
| 44. C34 | #67 | semidirect |
| 46. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 74. C22×C32 | #272 | semidirect |
| 75. C22×C32 | C32×D3 | semidirect |
| 85. C33 | C3×#67 | semidirect |
| 89. H(3,𝔽3) | C32×D4 | semidirect |
| 113. C22×C3 | C3×#272 | semidirect |
| 122. C32 | #6235 | direct (N × H) |
| 123. C32 | C32×#67 | semidirect |
| 138. C22 | C32×#272 | semidirect |
| 142. C3 | C3×#6235 | 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×C32×#272 | 2 |
| C32×#1084 | 2 |
| C33×#67 | 3 |
| C3×#6235 | 3 |