Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
196 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×C3×C9×C16 | C2 | semidirect |
| 3. C3×#63371 | C2 | semidirect |
| 5. #10588185 | C3 | direct (N × H) |
| 18. C2×C9×C16 | C2×C3 | semidirect |
| 19. #63371 | C2×C3 | semidirect |
| 55. C2×C3×C16 | D9 | semidirect |
| 112. C2×C16 | C3×D9 | semidirect |
| 113. C3×C9 | #350 | semidirect |
| 163. C9 | C3×#350 | semidirect |
| 186. C3 | #10588185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63464 | 2 |
| C2×C3×C9×C16 | 2 |
| C3×#63371 | 2 |
| C3×#4508 | 3 |
| #10588185 | 3 |