Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1352 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 1352 conjugacy classes of subgroups — too many to draw. Only its 136 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. #11757864 | C2 | direct (N × H) |
| 3. C2×C3×#1094 | C3 | semidirect |
| 4. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 9. C3×#1094 | C2×C3 | semidirect |
| 10. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 17. C2×C3×C22⋊C9 | C32 | semidirect |
| 36. C3×C22⋊C9 | C2×C32 | semidirect |
| 45. C23×C32 | 3−1+2 | semidirect |
| 81. C22×C32 | C2×3−1+2 | semidirect |
| 112. C2×C32 | #1094 | semidirect |
| 132. C32 | C2×#1094 | semidirect |
| 136. C23 | #6891 | semidirect |
| 151. C22 | C2×#6891 | semidirect |
| 158. C2 | #11757864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757864 | 2 |
| C23×C34 | 3 |
| C2×C3×#1094 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×#6891 | 4 |