Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
640 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 1. C2×#88524 | C2 | semidirect |
| 3. C4×#6226 | C2 | semidirect |
| 4. C3×C9×C4⋊C8 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 26. C9×C4⋊C8 | D3 | semidirect |
| 39. #6226 | D4 | semidirect |
| 68. C3×C4×C9 | SD16 | semidirect |
| 79. C3×C4⋊C8 | D9 | semidirect |
| 149. C4×C9 | #204 | semidirect |
| 157. C4⋊C8 | C3⋊D9 | semidirect |
| 159. C3×C9 | #460 | semidirect |
| 214. C3×C4 | #3664 | semidirect |
| 225. C9 | #4848 | semidirect |
| 254. C4 | #88524 | semidirect |
| 257. C3 | #10588512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| #11721711 | 2 |
| C4×#6226 | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720543 | 2 |
| #10592547 | 3 |
| #10588512 | 3 |