Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 1. C2×#88521 | C2 | semidirect |
| 3. C9×#812 | C2 | semidirect |
| 4. #11720235 | C2 | semidirect |
| 5. #11720233 | C2 | semidirect |
| 76. #812 | D9 | semidirect |
| 152. C3×C9 | #510 | semidirect |
| 214. C9 | #5195 | semidirect |
| 240. C3 | #10588589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C3×#63467 | 2 |
| C9×#812 | 2 |
| #11720235 | 2 |
| #11720233 | 2 |
| #10590638 | 3 |
| #10588589 | 3 |