Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1624 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 204 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. C32×C4×H(3,𝔽3) | C2 | semidirect |
| 3. C32×#1084 | C2 | semidirect |
| 5. C3×C4×#272 | C3 | direct (N × H) |
| 7. C32×#272 | C4 | direct (N × H) |
| 9. C34×C4 | D3 | semidirect |
| 13. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C3×#1084 | C2×C3 | semidirect |
| 15. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 19. C4×#272 | C32 | direct (N × H) |
| 24. C3×#272 | C3×C4 | direct (N × H) |
| 31. C33×C4 | C3×D3 | semidirect |
| 38. C4×H(3,𝔽3) | C2×C32 | semidirect |
| 39. #1084 | C2×C32 | semidirect |
| 40. C34 | C4×D3 | semidirect |
| 42. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 57. #272 | C32×C4 | direct (N × H) |
| 67. C32×C4 | #272 | direct (N × H) |
| 68. C32×C4 | C32×D3 | semidirect |
| 74. C33 | C3×C4×D3 | semidirect |
| 78. H(3,𝔽3) | C2×C32×C4 | semidirect |
| 99. C3×C4 | C3×#272 | direct (N × H) |
| 105. C32 | C4×#272 | direct (N × H) |
| 106. C32 | C32×C4×D3 | semidirect |
| 118. C4 | C32×#272 | direct (N × H) |
| 121. C3 | C3×C4×#272 | 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 |
| C32×C4×H(3,𝔽3) | 2 |
| C32×#1084 | 2 |
| C33×C4×D3 | 3 |
| C3×C4×#272 | 3 |