Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 459 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×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 3. #11722202 | C2 | semidirect |
| 4. #11722200 | C2 | semidirect |
| 5. #11722178 | C2 | semidirect |
| 100. C33 | #481 | semidirect |
| 137. C32 | #5034 | semidirect |
| 165. C3 | #10592733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#121 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #11722202 | 2 |
| #11722200 | 2 |
| #11722178 | 2 |
| #10592733 | 3 |