Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
940 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 175 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. #11721813 | C2 | semidirect |
| 3. C2×#88524 | C2 | semidirect |
| 4. C3×C9×C22⋊C8 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 13. C2×#6226 | C22 | semidirect |
| 14. C2×C3×C8×C9 | C22 | semidirect |
| 16. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 27. C9×C22⋊C8 | D3 | semidirect |
| 63. C2×C8×C9 | C2×D3 | semidirect |
| 70. C22×C3×C9 | SD16 | semidirect |
| 86. C3×C22⋊C8 | D9 | semidirect |
| 138. C2×C3×C8 | C2×D9 | semidirect |
| 162. C22×C9 | #204 | semidirect |
| 176. C22⋊C8 | C3⋊D9 | semidirect |
| 177. C3×C9 | #450 | semidirect |
| 225. C2×C8 | C2×C3⋊D9 | semidirect |
| 233. C22×C3 | #3664 | semidirect |
| 254. C9 | #4731 | semidirect |
| 286. C22 | #88524 | semidirect |
| 292. C3 | #10588413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D9) | 2 |
| #11721813 | 2 |
| C2×#88524 | 2 |
| C3×C9×C22⋊C8 | 2 |
| #11720543 | 2 |
| #10592430 | 3 |
| #10588413 | 3 |