Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. C2×#88399 | C2 | semidirect |
| 2. #11720179 | C2 | semidirect |
| 3. C2×D216 | C2 | semidirect |
| 4. C2×#88360 | C2 | semidirect |
| 5. C27×C22⋊C8 | C2 | semidirect |
| 6. #11720061 | C2 | semidirect |
| 7. #11720057 | C2 | semidirect |
| 45. D108 | D4 | semidirect |
| 48. Dic54 | D4 | semidirect |
| 152. C22⋊C8 | D27 | semidirect |
| 153. C27 | #449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88399 | 2 |
| #11720179 | 2 |
| C2×D216 | 2 |
| C2×#88360 | 2 |
| C27×C22⋊C8 | 2 |
| #11720061 | 2 |
| #11720057 | 2 |
| #10588416 | 3 |