Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
362 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 66. C3×C4×C9 | Q16 | semidirect |
| 152. C4×C9 | #216 | semidirect |
| 161. C3×C9 | #462 | semidirect |
| 219. C3×C4 | #3674 | semidirect |
| 230. C9 | #5090 | semidirect |
| 256. C4 | #88427 | semidirect |
| 260. C3 | #10588707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×Dic6 | 2 |
| C3×#63431 | 2 |
| C2×#88427 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720268 | 2 |
| #10590384 | 3 |
| #10588707 | 3 |