Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1144 conjugacy classes of subgroups; only the 484 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 484 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. #11758099 | C2 | direct (N × H) |
| 3. C2×C3×#1094 | C3 | semidirect |
| 4. C2×#66437 | C3 | semidirect |
| 9. C3×#1094 | C2×C3 | semidirect |
| 10. #66437 | C2×C3 | semidirect |
| 15. C2×#1094 | C32 | semidirect |
| 16. C2×C3×C22⋊C9 | C32 | semidirect |
| 29. #1094 | C2×C32 | semidirect |
| 30. C3×C22⋊C9 | C2×C32 | semidirect |
| 88. C23 | 3−1+4 | semidirect |
| 100. C22 | C2×3−1+4 | semidirect |
| 106. C2 | #11758099 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758099 | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×#66437 | 3 |
| C2×3−1+4 | 4 |