Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
256 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11757407 | C2 | direct (N × H) |
| 17. C2×#1094 | C9 | semidirect |
| 35. #1094 | C2×C9 | semidirect |
| 156. C23 | 3−1+2⋊C9 | semidirect |
| 177. C22 | C2×3−1+2⋊C9 | semidirect |
| 186. C2 | #11757407 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757407 | 2 |
| C2×C3×#1094 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C23×C32⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×3−1+2⋊C9 | 4 |