Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
539 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 539 conjugacy classes of subgroups — too many to draw. Only its 102 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. #63511⋊C3 | C2 | semidirect |
| 3. #63498⋊C3 | C2 | semidirect |
| 4. #63396⋊C3 | C2 | semidirect |
| 5. #63391⋊C3 | C2 | semidirect |
| 7. #10588921 | C3 | semidirect |
| 13. C2×3−1+2⋊Q8 | C22 | semidirect |
| 17. C4×3−1+2⋊C4 | C22 | semidirect |
| 18. #3667⋊C3 | C22 | semidirect |
| 26. #63511 | C2×C3 | semidirect |
| 27. #63498 | C2×C3 | semidirect |
| 28. #63396 | C2×C3 | semidirect |
| 29. #63391 | C2×C3 | semidirect |
| 67. C2×Dic18 | C22×C3 | semidirect |
| 71. C4×Dic9 | C22×C3 | semidirect |
| 72. #3667 | C22×C3 | semidirect |
| 187. 3−1+2 | #455 | semidirect |
| 259. C9 | C3×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×H(5,𝔽2) | 2 |
| #63511⋊C3 | 2 |
| #63498⋊C3 | 2 |
| #63396⋊C3 | 2 |
| #63391⋊C3 | 2 |
| C3×#5242 | 3 |
| #10588921 | 3 |