Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
406 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4×#6226 | C2 | semidirect |
| 3. C2×#88418 | C2 | semidirect |
| 5. C9×C4⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 111. C4⋊(C3⋊C8) | D9 | semidirect |
| 221. C3×C9 | #464 | semidirect |
| 314. C9 | #5054 | semidirect |
| 353. C3 | #10588529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6226 | 2 |
| C3×#63437 | 2 |
| C2×#88418 | 2 |
| C2×#88415 | 2 |
| C9×C4⋊(C3⋊C8) | 2 |
| #11720283 | 2 |
| #11720276 | 2 |
| #10590378 | 3 |
| #10588529 | 3 |