Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 374 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. C4×C9×Dic6 | C2 | semidirect |
| 3. C2×#88427 | C2 | semidirect |
| 5. C4⋊(C3⋊(C9⋊C8)) | C2 | semidirect |
| 6. #11720268 | C2 | semidirect |
| 102. C4×Dic6 | D9 | semidirect |
| 213. C3×C9 | #464 | semidirect |
| 302. C9 | #5054 | semidirect |
| 341. C3 | #10588711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63437 | 2 |
| C4×C9×Dic6 | 2 |
| C2×#88427 | 2 |
| C2×#88425 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720268 | 2 |
| #11720266 | 2 |
| #10590267 | 3 |
| #10588711 | 3 |