Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 800 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 |
|---|---|---|
| 2. C3×#63486 | C2 | semidirect |
| 3. C2×#88416 | C2 | semidirect |
| 4. C9×#830 | C2 | semidirect |
| 5. #11720284 | C2 | semidirect |
| 13. C2×C3×Dic18 | C22 | semidirect |
| 15. C3×C4⋊Dic9 | C22 | semidirect |
| 17. C2×C9×C3⋊C8 | C22 | semidirect |
| 26. #63486 | D3 | semidirect |
| 68. C2×Dic18 | C2×D3 | semidirect |
| 71. C4⋊Dic9 | C2×D3 | semidirect |
| 76. C22×C3×C9 | SD16 | semidirect |
| 94. #830 | D9 | semidirect |
| 169. C2×C3⋊C8 | C2×D9 | semidirect |
| 189. C22×C9 | #215 | semidirect |
| 210. C3×C9 | #450 | semidirect |
| 286. C22×C3 | #3664 | semidirect |
| 314. C9 | #5046 | semidirect |
| 351. C22 | #88416 | semidirect |
| 358. C3 | #10588413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D9) | 2 |
| C3×#63486 | 2 |
| C2×#88416 | 2 |
| C9×#830 | 2 |
| #11720284 | 2 |
| #10591183 | 3 |
| #10588413 | 3 |