Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
638 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #11721813 | C2 | semidirect |
| 3. C2×#88415 | C2 | semidirect |
| 4. C9×#830 | C2 | semidirect |
| 5. #11720283 | C2 | semidirect |
| 10. C2×#6226 | C22 | semidirect |
| 15. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 17. C2×C9×C3⋊C8 | C22 | semidirect |
| 76. C22×C3×C9 | SD16 | semidirect |
| 95. #830 | D9 | semidirect |
| 165. C2×C3⋊C8 | C2×D9 | semidirect |
| 185. C22×C9 | #214 | semidirect |
| 204. C3×C9 | #450 | semidirect |
| 279. C22×C3 | #3664 | semidirect |
| 301. C9 | #5218 | semidirect |
| 337. C22 | #88415 | semidirect |
| 344. C3 | #10588413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D36 | 2 |
| #11721813 | 2 |
| C2×#88415 | 2 |
| C9×#830 | 2 |
| #11720283 | 2 |
| #10591172 | 3 |
| #10588413 | 3 |