Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
532 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11721836 | C2 | semidirect |
| 3. #11720891 | C2 | semidirect |
| 4. C3×#63391 | C2 | semidirect |
| 5. #11720300 | C2 | semidirect |
| 9. C2×#6226 | C22 | semidirect |
| 15. C4×C3⋊Dic9 | C22 | semidirect |
| 16. C3×#3667 | C22 | semidirect |
| 29. #63391 | D3 | semidirect |
| 71. #3667 | C2×D3 | semidirect |
| 186. C3×C9 | #455 | semidirect |
| 269. C9 | #4746 | semidirect |
| 305. C3 | #10588921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| #11721836 | 2 |
| #11720891 | 2 |
| C3×#63391 | 2 |
| #11720300 | 2 |
| #10591513 | 3 |
| #10588921 | 3 |