Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
556 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 106 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. #11757832 | C2 | direct (N × H) |
| 3. C2×C3×#1094 | C3 | semidirect |
| 4. C2×C32×C22⋊C9 | C3 | semidirect |
| 5. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 6. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 12. C32×C22⋊C9 | C2×C3 | semidirect |
| 13. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 14. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 55. C23×C32 | 3−1+2 | semidirect |
| 59. C2×C22⋊C9 | H(3,𝔽3) | semidirect |
| 93. C22×C32 | C2×3−1+2 | semidirect |
| 97. C22⋊C9 | C2×H(3,𝔽3) | semidirect |
| 130. C2×C32 | #1094 | semidirect |
| 155. C32 | C2×#1094 | semidirect |
| 160. C23 | C9⋊H(3,𝔽3) | semidirect |
| 178. C22 | C2×C9⋊H(3,𝔽3) | semidirect |
| 186. C2 | #11757832 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757832 | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×C9⋊H(3,𝔽3) | 4 |