Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
432 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
| 4. #11720932 | C2 | semidirect |
| 5. C2×#88418 | C2 | semidirect |
| 7. C9×#815 | C2 | semidirect |
| 109. #815 | D9 | semidirect |
| 214. C3×C9 | #497 | semidirect |
| 301. C9 | #5167 | semidirect |
| 336. C3 | #10588396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C2×C3×#3664 | 2 |
| #11720948 | 2 |
| #11720932 | 2 |
| C2×#88418 | 2 |
| C2×#88415 | 2 |
| C9×#815 | 2 |
| #10590897 | 3 |
| #10588396 | 3 |