Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
924 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 221 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. #11724517 | C2 | semidirect |
| 3. #11724515 | C2 | semidirect |
| 4. #11724511 | C2 | semidirect |
| 5. C2×#88989 | C2 | semidirect |
| 14. #88993 | C22 | semidirect |
| 15. C2×C3⋊#622 | C22 | semidirect |
| 18. #88989 | C22 | semidirect |
| 19. #88988 | C22 | semidirect |
| 155. C33 | #568 | semidirect |
| 229. C32 | #5819 | semidirect |
| 264. C3 | #10596648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#41×C3⋊D3 | 2 |
| #11724517 | 2 |
| #11724515 | 2 |
| #11724511 | 2 |
| C2×#88989 | 2 |
| #10596648 | 3 |
| #5819 | 9 |