Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
736 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 91 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. H(3,𝔽3)×C3⋊D9 | C2 | semidirect |
| 2. C3×D9×H(3,𝔽3) | C2 | semidirect |
| 3. D3×C9×H(3,𝔽3) | C2 | semidirect |
| 5. C32×D3×D9 | C3 | semidirect |
| 7. C3×C9×H(3,𝔽3) | C22 | semidirect |
| 9. C32×C3⋊D9 | C2×C3 | semidirect |
| 12. C32×D3×C9 | C2×C3 | semidirect |
| 13. C33×D9 | C2×C3 | semidirect |
| 18. D9×H(3,𝔽3) | D3 | direct (N × H) |
| 27. C33×C9 | C22×C3 | semidirect |
| 31. C9×H(3,𝔽3) | C2×D3 | semidirect |
| 47. D3×H(3,𝔽3) | D9 | direct (N × H) |
| 57. C32×D9 | C3×D3 | semidirect |
| 67. D3×D9 | H(3,𝔽3) | direct (N × H) |
| 73. C3×H(3,𝔽3) | C2×D9 | semidirect |
| 83. C32×C9 | C2×C3×D3 | semidirect |
| 103. C32×D3 | C3×D9 | semidirect |
| 114. C3⋊D9 | C2×H(3,𝔽3) | semidirect |
| 117. D3×C9 | C2×H(3,𝔽3) | semidirect |
| 125. C3×D9 | C2×H(3,𝔽3) | semidirect |
| 142. C33 | C2×C3×D9 | semidirect |
| 149. H(3,𝔽3) | D3×D9 | direct (N × H) |
| 166. C3×C9 | C22×H(3,𝔽3) | semidirect |
| 201. D9 | D3×H(3,𝔽3) | direct (N × H) |
| 225. C32 | C3×D3×D9 | semidirect |
| 234. C9 | C2×D3×H(3,𝔽3) | semidirect |
| 251. D3 | D9×H(3,𝔽3) | direct (N × H) |
| 261. C3 | C2×D9×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C3⋊D9 | 2 |
| C3×D9×H(3,𝔽3) | 2 |
| D3×C9×H(3,𝔽3) | 2 |
| D32×H(3,𝔽3) | 3 |
| C32×D3×D9 | 3 |
| C2×D9×H(3,𝔽3) | 3 |