Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
404 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #11720278 | C2 | semidirect |
| 5. #11720276 | C2 | semidirect |
| 165. C3×C9 | #483 | semidirect |
| 240. C9 | #5043 | semidirect |
| 273. C3 | #10588401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊Dic9) | 2 |
| C3×#63486 | 2 |
| C9×#830 | 2 |
| #11720278 | 2 |
| #11720276 | 2 |
| #10591126 | 3 |
| #10588401 | 3 |