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×#88415 | C2 | semidirect |
| 4. C9×#830 | C2 | semidirect |
| 5. #11720277 | C2 | semidirect |
| 39. #6226 | D4 | semidirect |
| 75. C22×C3×C9 | SD16 | semidirect |
| 92. #830 | D9 | semidirect |
| 182. C22×C9 | #214 | semidirect |
| 199. C3×C9 | #448 | semidirect |
| 273. C22×C3 | #3664 | semidirect |
| 293. C9 | #5040 | semidirect |
| 327. C22 | #88415 | semidirect |
| 334. C3 | #10588404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6226 | 2 |
| C3×#63492 | 2 |
| C2×#88415 | 2 |
| C9×#830 | 2 |
| #11720277 | 2 |
| #10591181 | 3 |
| #10588404 | 3 |