Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
366 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C2×C3×Dic36 | C2 | semidirect |
| 4. #11720540 | C2 | semidirect |
| 5. #11720276 | C2 | semidirect |
| 24. C2×Dic36 | D3 | semidirect |
| 154. C3×C9 | #470 | semidirect |
| 219. C9 | #5189 | semidirect |
| 248. C3 | #10588807 | 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 |
| C2×C3×Dic36 | 2 |
| #11720960 | 2 |
| #11720540 | 2 |
| #11720276 | 2 |
| #10590854 | 3 |
| #10588807 | 3 |