Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×Dic54 | C2 | semidirect |
| 3. C27×#117 | C2 | semidirect |
| 4. #11720146 | C2 | semidirect |
| 5. #11720135 | C2 | semidirect |
| 6. #11720124 | C2 | semidirect |
| 7. #11720118 | C2 | semidirect |
| 130. #117 | D27 | semidirect |
| 131. C27 | #536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88399 | 2 |
| C22×Dic54 | 2 |
| C27×#117 | 2 |
| #11720146 | 2 |
| #11720135 | 2 |
| #11720124 | 2 |
| #11720118 | 2 |
| #10589628 | 3 |