Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
614 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 614 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. C9×#924 | C2 | semidirect |
| 3. C2×#88425 | C2 | semidirect |
| 4. #11720571 | C2 | semidirect |
| 5. #11720266 | C2 | semidirect |
| 13. C2×C9×Dic6 | C22 | semidirect |
| 14. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 16. C9×C4⋊Dic3 | C22 | semidirect |
| 73. C22×C3×C9 | SD16 | semidirect |
| 88. #924 | D9 | semidirect |
| 147. C2×Dic6 | C2×D9 | semidirect |
| 154. C4⋊Dic3 | C2×D9 | semidirect |
| 177. C22×C9 | #214 | semidirect |
| 194. C3×C9 | #450 | semidirect |
| 267. C22×C3 | #3675 | semidirect |
| 287. C9 | #5218 | semidirect |
| 323. C22 | #88425 | semidirect |
| 330. C3 | #10588729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D36 | 2 |
| C9×#924 | 2 |
| C2×#88425 | 2 |
| #11720571 | 2 |
| #11720266 | 2 |
| #10591169 | 3 |
| #10588729 | 3 |