Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
630 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×#6226 | C2 | semidirect |
| 3. C2×#88424 | C2 | semidirect |
| 4. C3×#63389 | C2 | semidirect |
| 5. #11720269 | C2 | semidirect |
| 28. #63389 | D3 | semidirect |
| 39. #6226 | D4 | semidirect |
| 75. C22×C3×C9 | SD16 | semidirect |
| 185. C22×C9 | #204 | semidirect |
| 199. C3×C9 | #448 | semidirect |
| 273. C22×C3 | #3672 | semidirect |
| 293. C9 | #4738 | semidirect |
| 327. C22 | #88424 | semidirect |
| 334. C3 | #10588716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6226 | 2 |
| C9×#930 | 2 |
| C2×#88424 | 2 |
| C3×#63389 | 2 |
| #11720269 | 2 |
| #10591181 | 3 |
| #10588716 | 3 |