Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
520 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 4. #10589331 | C3 | direct (N × H) |
| 115. C33 | #330 | semidirect |
| 167. C32 | #4465 | semidirect |
| 168. C32 | C3×#330 | semidirect |
| 192. C3 | C3×#4465 | semidirect |
| 193. C3 | #10589331 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64079 | 2 |
| C33×#97 | 2 |
| C3×#63630 | 2 |
| #10589331 | 3 |
| C3×#4465 | 3 |