Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
1124 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 316 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 |
|---|---|---|
| 4. #11757845 | C3 | semidirect |
| 5. #11757844 | C3 | semidirect |
| 6. #11757843 | C3 | semidirect |
| 7. 3−1+2×C22⋊C9 | C3 | semidirect |
| 8. #11757821 | C3 | semidirect |
| 9. C9×#1094 | C3 | semidirect |
| 29. C9⋊(C22⋊C9) | C32 | semidirect |
| 30. (C22⋊C9)⋊C9 | C32 | semidirect |
| 31. (C22⋊C9)⋊C9 | C32 | semidirect |
| 32. C9×C22⋊C9 | C32 | semidirect |
| 59. C22×3−1+2 | 3−1+2 | semidirect |
| 67. #1094 | 3−1+2 | direct (N × H) |
| 122. C22×C9 | C3×3−1+2 | semidirect |
| 125. C22⋊C9 | C3×3−1+2 | semidirect |
| 141. 3−1+2 | #1094 | direct (N × H) |
| 190. C9 | C3×#1094 | semidirect |
| 198. C22 | 3−1+22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×3−1+2 | 3 |
| C32×#1094 | 3 |
| #11757864 | 3 |
| #11757845 | 3 |
| #11757844 | 3 |
| #11757843 | 3 |
| 3−1+2×C22⋊C9 | 3 |
| #11757821 | 3 |
| C9×#1094 | 3 |
| 3−1+22 | 4 |