Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2632 conjugacy classes of subgroups; only the 571 normal subgroups are shown.
This group has 2632 conjugacy classes of subgroups — too many to draw. Only its 571 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. C2×#88861 | C2 | semidirect |
| 3. #11723965 | C2 | semidirect |
| 4. #11722202 | C2 | semidirect |
| 5. #11722200 | C2 | semidirect |
| 12. C2×#6308 | C22 | semidirect |
| 15. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 17. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 56. C22×C33 | SD16 | semidirect |
| 105. C22×C32 | #214 | semidirect |
| 116. C33 | #450 | semidirect |
| 154. C22×C3 | #3754 | semidirect |
| 160. C32 | #5218 | semidirect |
| 187. C22 | #88861 | semidirect |
| 193. C3 | #10592917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| C2×#88861 | 2 |
| #11723965 | 2 |
| #11722202 | 2 |
| #11722200 | 2 |
| #10592917 | 3 |