Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
554 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 7. #10590291 | C3 | direct (N × H) |
| 178. C33 | #491 | semidirect |
| 262. C32 | #5069 | semidirect |
| 263. C32 | #5082 | semidirect |
| 264. C32 | C3×#491 | semidirect |
| 294. C3 | #10590291 | direct (N × H) |
| 295. C3 | C3×#5069 | semidirect |
| 296. C3 | C3×#5082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#870 | 2 |
| C32×#869 | 2 |
| C3×#63630 | 2 |
| C3×#63565 | 2 |
| C3×#5082 | 3 |
| C3×#5069 | 3 |
| #10590291 | 3 |