Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 1208 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11757461 | C2 | direct (N × H) |
| 3. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 8. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 13. C23×C33 | C9 | semidirect |
| 33. C22×C33 | C2×C9 | semidirect |
| 60. C2×C33 | C22⋊C9 | semidirect |
| 91. C33 | C2×C22⋊C9 | semidirect |
| 148. C23 | #6866 | semidirect |
| 166. C22 | C2×#6866 | semidirect |
| 174. C2 | #11757461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757461 | 2 |
| C23×C34 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×#6866 | 4 |