Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
434 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 434 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. C22×C9×H(3,𝔽3) | C2 | semidirect |
| 2. C2×D9×H(3,𝔽3) | C2 | semidirect |
| 3. H(3,𝔽3)×Dic9 | C2 | semidirect |
| 5. C32×#611 | C3 | semidirect |
| 10. C22×C32×C9 | C2×C3 | semidirect |
| 12. C2×C32×D9 | C2×C3 | semidirect |
| 14. C32×Dic9 | C2×C3 | semidirect |
| 16. C9×H(3,𝔽3) | D4 | semidirect |
| 34. C22×H(3,𝔽3) | D9 | semidirect |
| 45. C32×C9 | C3×D4 | semidirect |
| 50. #611 | H(3,𝔽3) | direct (N × H) |
| 73. C22×C32 | C3×D9 | semidirect |
| 82. C22×C9 | C2×H(3,𝔽3) | semidirect |
| 83. C2×D9 | C2×H(3,𝔽3) | semidirect |
| 84. Dic9 | C2×H(3,𝔽3) | semidirect |
| 87. H(3,𝔽3) | #611 | direct (N × H) |
| 129. C32 | C3×#611 | semidirect |
| 133. C9 | D4×H(3,𝔽3) | semidirect |
| 149. C22 | D9×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×H(3,𝔽3) | 2 |
| C2×D9×H(3,𝔽3) | 2 |
| H(3,𝔽3)×Dic9 | 2 |
| #67×H(3,𝔽3) | 3 |
| C32×#611 | 3 |