Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
850 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 3. C2×C9×Dic12 | C2 | semidirect |
| 4. C2×C3×Dic36 | C2 | semidirect |
| 5. C2×#88427 | C2 | semidirect |
| 6. #11720829 | C2 | direct (N × H) |
| 19. C9×Dic12 | C22 | semidirect |
| 20. C3×Dic36 | C22 | semidirect |
| 21. #88427 | C22 | semidirect |
| 34. C2×Dic36 | D3 | semidirect |
| 81. Dic36 | C2×D3 | semidirect |
| 83. C2×C3⋊D9 | Q16 | semidirect |
| 99. C2×Dic12 | D9 | semidirect |
| 141. C2×C3×C9 | C2×Q16 | semidirect |
| 143. C3⋊D9 | C2×Q16 | semidirect |
| 170. Dic12 | C2×D9 | semidirect |
| 202. C3×C9 | C22×Q16 | semidirect |
| 245. C2×C9 | D3×Q16 | semidirect |
| 286. C9 | C2×D3×Q16 | semidirect |
| 304. C2×C3 | Q16×D9 | semidirect |
| 320. C3 | C2×Q16×D9 | semidirect |
| 323. C2 | #11720829 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C3⋊D9)⋊Q8 | 2 |
| C2×C8×C3⋊D9 | 2 |
| C2×C9×Dic12 | 2 |
| C2×C3×Dic36 | 2 |
| C2×#88427 | 2 |
| #11720829 | 2 |
| C2×#63802 | 3 |
| C2×Q16×D9 | 3 |