Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 405 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. #11723977 | C2 | semidirect |
| 3. D4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C2×#88861 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722186 | C2 | semidirect |
| 7. #11722184 | C2 | semidirect |
| 134. C33 | #463 | semidirect |
| 182. C32 | #5153 | semidirect |
| 217. C3 | #10592852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| #11723977 | 2 |
| D4×C3⋊(C3⋊Dic3) | 2 |
| C2×#88861 | 2 |
| #11722202 | 2 |
| #11722186 | 2 |
| #11722184 | 2 |
| #10592852 | 3 |