Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
290 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 290 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 |
|---|---|---|
| 8. C3×C9×Q16 | C4 | semidirect |
| 35. C9×Q16 | Dic3 | semidirect |
| 72. C3×Q16 | Dic9 | semidirect |
| 93. C3×C9 | #358 | semidirect |
| 116. Q16 | C3⋊Dic9 | semidirect |
| 131. C9 | #4564 | semidirect |
| 150. C3 | #10588241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| #11720541 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| #10589430 | 3 |
| #10588241 | 3 |