Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
874 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 169 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×#88634 | C2 | semidirect |
| 2. C2×C8×C3⋊D9 | C2 | semidirect |
| 3. C2×C9×Dic12 | C2 | semidirect |
| 4. C2×C3×D72 | C2 | semidirect |
| 5. C2×#88425 | C2 | semidirect |
| 6. #11720831 | C2 | direct (N × H) |
| 15. #88634 | C22 | semidirect |
| 18. C8×C3⋊D9 | C22 | semidirect |
| 19. C9×Dic12 | C22 | semidirect |
| 20. C3×D72 | C22 | semidirect |
| 21. #88425 | C22 | semidirect |
| 32. C2×D72 | D3 | semidirect |
| 79. D72 | C2×D3 | semidirect |
| 99. C2×Dic12 | D9 | semidirect |
| 142. C2×C3×C9 | #135 | semidirect |
| 171. Dic12 | C2×D9 | semidirect |
| 206. C3×C9 | C2×#135 | semidirect |
| 250. C2×C9 | #912 | semidirect |
| 294. C9 | C2×#912 | semidirect |
| 313. C2×C3 | #63481 | semidirect |
| 331. C3 | C2×#63481 | semidirect |
| 335. C2 | #11720831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88634 | 2 |
| C2×C8×C3⋊D9 | 2 |
| C2×C9×Dic12 | 2 |
| C2×C3×D72 | 2 |
| C2×#88425 | 2 |
| #11720831 | 2 |
| C2×#63810 | 3 |
| C2×#63481 | 3 |