Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
384 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #11720138 | C2 | semidirect |
| 5. #11720119 | C2 | semidirect |
| 6. #11720118 | C2 | semidirect |
| 7. C4×Dic54 | C2 | semidirect |
| 110. C27 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×#117 | 2 |
| #11720173 | 2 |
| #11720138 | 2 |
| #11720128 | 2 |
| #11720119 | 2 |
| #11720118 | 2 |
| C4×Dic54 | 2 |
| #10589620 | 3 |