Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
392 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11721867 | C2 | semidirect |
| 2. C9×#949 | C2 | semidirect |
| 3. C3×#63510 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. #11720296 | C2 | semidirect |
| 6. #11720288 | C2 | semidirect |
| 7. #11720285 | C2 | semidirect |
| 35. #63510 | D3 | semidirect |
| 107. #949 | D9 | semidirect |
| 231. C3×C9 | #472 | semidirect |
| 329. C9 | #5142 | semidirect |
| 370. C3 | #10588880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721867 | 2 |
| C9×#949 | 2 |
| C3×#63510 | 2 |
| C2×#88422 | 2 |
| #11720296 | 2 |
| #11720288 | 2 |
| #11720285 | 2 |
| #10591677 | 3 |
| #10588880 | 3 |