Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
389 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 389 conjugacy classes of subgroups — too many to draw. Only its 72 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. Dic9⋊H(3,𝔽3) | C2 | semidirect |
| 4. C3×#611⋊C3 | C3 | semidirect |
| 6. C32×#611 | C3 | semidirect |
| 10. C22×C3×3−1+2 | C2×C3 | semidirect |
| 12. C22×C32×C9 | C2×C3 | semidirect |
| 13. C2×C3×AGL(1,ℤ/9) | C2×C3 | semidirect |
| 15. C2×C32×D9 | C2×C3 | semidirect |
| 16. C3×3−1+2⋊C4 | C2×C3 | semidirect |
| 18. C32×Dic9 | C2×C3 | semidirect |
| 21. C9⋊H(3,𝔽3) | D4 | semidirect |
| 64. C3×3−1+2 | C3×D4 | semidirect |
| 66. C32×C9 | C3×D4 | semidirect |
| 74. #611 | H(3,𝔽3) | semidirect |
| 111. C22×C32 | AGL(1,ℤ/9) | semidirect |
| 124. C22×C9 | C2×H(3,𝔽3) | semidirect |
| 125. C2×D9 | C2×H(3,𝔽3) | semidirect |
| 126. Dic9 | C2×H(3,𝔽3) | semidirect |
| 192. C32 | #611⋊C3 | semidirect |
| 197. C9 | D4×H(3,𝔽3) | semidirect |
| 216. 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 |
| Dic9⋊H(3,𝔽3) | 2 |
| C3×#611⋊C3 | 3 |
| #67×H(3,𝔽3) | 3 |
| C32×#611 | 3 |