Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
392 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 131 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. #11720193 | C2 | semidirect |
| 4. #11720128 | C2 | semidirect |
| 5. #11720127 | C2 | semidirect |
| 6. #11720119 | C2 | semidirect |
| 109. C27 | #563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×#124 | 2 |
| #11720193 | 2 |
| #11720184 | 2 |
| #11720128 | 2 |
| #11720127 | 2 |
| #11720119 | 2 |
| #10589774 | 3 |