Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1928 conjugacy classes of subgroups; only the 308 normal subgroups are shown.
This group has 1928 conjugacy classes of subgroups — too many to draw. Only its 308 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×#1084 | C2 | direct (N × H) |
| 4. C2×C3×#1084 | C3 | direct (N × H) |
| 5. C2×C32×H(3,𝔽3) | C4 | semidirect |
| 11. C3×#1084 | C2×C3 | direct (N × H) |
| 12. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 16. C2×#1084 | C32 | direct (N × H) |
| 17. C2×C34 | Dic3 | semidirect |
| 21. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 33. #1084 | C2×C32 | direct (N × H) |
| 34. C34 | C2×Dic3 | semidirect |
| 36. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 45. C2×C33 | C3×Dic3 | semidirect |
| 53. C2×H(3,𝔽3) | C32×C4 | semidirect |
| 67. C33 | C2×C3×Dic3 | semidirect |
| 71. H(3,𝔽3) | C2×C32×C4 | semidirect |
| 81. C2×C32 | #1084 | direct (N × H) |
| 83. C2×C32 | C32×Dic3 | semidirect |
| 97. C32 | C2×#1084 | direct (N × H) |
| 98. C32 | C2×C32×Dic3 | semidirect |
| 105. C2×C3 | C3×#1084 | direct (N × H) |
| 113. C3 | C2×C3×#1084 | direct (N × H) |
| 115. C2 | C32×#1084 | 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 |
| C32×#1084 | 2 |
| C2×C33×Dic3 | 3 |
| C2×C3×#1084 | 3 |