Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
366 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×D9×H(3,𝔽3) | C2 | semidirect |
| 2. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 4. C32×D36 | C3 | semidirect |
| 8. C2×C32×D9 | C2×C3 | semidirect |
| 10. C32×C4×C9 | C2×C3 | semidirect |
| 12. C9×H(3,𝔽3) | D4 | semidirect |
| 28. C4×H(3,𝔽3) | D9 | semidirect |
| 34. C32×C9 | C3×D4 | semidirect |
| 39. D36 | H(3,𝔽3) | direct (N × H) |
| 57. C32×C4 | C3×D9 | semidirect |
| 59. C2×D9 | C2×H(3,𝔽3) | semidirect |
| 62. C4×C9 | C2×H(3,𝔽3) | semidirect |
| 65. H(3,𝔽3) | D36 | direct (N × H) |
| 96. C32 | C3×D36 | semidirect |
| 100. C9 | D4×H(3,𝔽3) | semidirect |
| 111. C4 | D9×H(3,𝔽3) | semidirect |
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 |
| D12×H(3,𝔽3) | 3 |
| C32×D36 | 3 |