Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
230 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 2. C3×C9×#101 | C2 | semidirect |
| 3. C3×#63394 | C2 | semidirect |
| 5. #10588155 | C3 | direct (N × H) |
| 18. C9×#101 | C2×C3 | semidirect |
| 19. #63394 | C2×C3 | semidirect |
| 58. C3×#101 | D9 | semidirect |
| 124. #101 | C3×D9 | semidirect |
| 125. C3×C9 | #355 | semidirect |
| 184. C9 | C3×#355 | semidirect |
| 210. C3 | #10588155 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63509 | 2 |
| C3×C9×#101 | 2 |
| C3×#63394 | 2 |
| C3×#4477 | 3 |
| #10588155 | 3 |