Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
366 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 98 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. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 3. H(3,𝔽3)×Dic9 | C2 | semidirect |
| 5. C32×C4×D9 | C3 | semidirect |
| 7. D9×H(3,𝔽3) | C4 | direct (N × H) |
| 11. C32×C4×C9 | C2×C3 | semidirect |
| 13. C32×Dic9 | C2×C3 | semidirect |
| 15. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 23. C32×D9 | C3×C4 | semidirect |
| 33. C4×H(3,𝔽3) | D9 | direct (N × H) |
| 41. C32×C9 | C2×C3×C4 | semidirect |
| 46. C4×D9 | H(3,𝔽3) | direct (N × H) |
| 65. C32×C4 | C3×D9 | semidirect |
| 72. C4×C9 | C2×H(3,𝔽3) | semidirect |
| 73. Dic9 | C2×H(3,𝔽3) | semidirect |
| 76. H(3,𝔽3) | C4×D9 | direct (N × H) |
| 95. D9 | C4×H(3,𝔽3) | direct (N × H) |
| 110. C32 | C3×C4×D9 | semidirect |
| 114. C9 | C2×C4×H(3,𝔽3) | semidirect |
| 126. C4 | D9×H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×H(3,𝔽3) | 2 |
| C4×C9×H(3,𝔽3) | 2 |
| H(3,𝔽3)×Dic9 | 2 |
| C4×D3×H(3,𝔽3) | 3 |
| C32×C4×D9 | 3 |