Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #11720535 | C2 | semidirect |
| 4. C3×#63372 | C2 | semidirect |
| 5. #11720280 | C2 | semidirect |
| 26. #63372 | D3 | semidirect |
| 136. C3×C9 | #430 | semidirect |
| 191. C9 | #4893 | semidirect |
| 216. C3 | #10588800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×ΓL(1,𝔽25) | 2 |
| D3×#3667 | 2 |
| #11720535 | 2 |
| C3×#63372 | 2 |
| #11720280 | 2 |
| #10590912 | 3 |
| #10588800 | 3 |