Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
400 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 6. C2×C3×Q8×C9 | C4 | semidirect |
| 10. C3×C9×C4⋊C4 | C4 | semidirect |
| 39. C2×Q8×C9 | Dic3 | semidirect |
| 43. C9×C4⋊C4 | Dic3 | semidirect |
| 90. C2×C3×Q8 | Dic9 | semidirect |
| 98. C3×C4⋊C4 | Dic9 | semidirect |
| 127. C3×C9 | #328 | semidirect |
| 160. C2×Q8 | C3⋊Dic9 | semidirect |
| 165. C4⋊C4 | C3⋊Dic9 | semidirect |
| 188. C9 | #4538 | semidirect |
| 220. C3 | #10588215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C22⋊Q8 | 2 |
| #11720572 | 2 |
| #11720571 | 2 |
| #10589404 | 3 |
| #10588215 | 3 |