Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1344 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 349 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. #11723931 | C2 | semidirect |
| 5. #11722186 | C2 | semidirect |
| 6. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 7. #11722180 | C2 | semidirect |
| 117. C33 | #488 | semidirect |
| 157. C32 | #4768 | semidirect |
| 186. C3 | #10592467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723977 | 2 |
| #11723931 | 2 |
| C33×#102 | 2 |
| #11722202 | 2 |
| #11722186 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #11722180 | 2 |
| #10592467 | 3 |