Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 13. #88370 | C4 | semidirect |
| 115. C27 | #441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic27 | 2 |
| C2×#88370 | 2 |
| #11720136 | 2 |
| C27×#103 | 2 |
| #11720057 | 2 |
| #11720056 | 2 |
| #11720048 | 2 |
| #10588469 | 3 |