Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
436 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 436 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 |
|---|---|---|
| 2. C2×C3×C4⋊Dic9 | C2 | semidirect |
| 3. C9×#830 | C2 | semidirect |
| 4. #11720284 | C2 | semidirect |
| 5. #11720278 | C2 | semidirect |
| 24. C2×C4⋊Dic9 | D3 | semidirect |
| 81. #830 | D9 | semidirect |
| 182. C3×C9 | #481 | semidirect |
| 271. C9 | #4968 | semidirect |
| 310. C3 | #10588417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721819 | 2 |
| C2×C3×C4⋊Dic9 | 2 |
| C9×#830 | 2 |
| #11720284 | 2 |
| #11720278 | 2 |
| #10591125 | 3 |
| #10588417 | 3 |