Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
688 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 688 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 |
|---|---|---|
| 1. C22×C3×D36 | C2 | semidirect |
| 2. #11721819 | C2 | semidirect |
| 3. C2×#88417 | C2 | semidirect |
| 4. C9×#830 | C2 | semidirect |
| 5. #11720283 | C2 | semidirect |
| 11. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 16. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 17. C2×C9×C3⋊C8 | C22 | semidirect |
| 22. C22×D36 | D3 | semidirect |
| 44. C3×D36 | D4 | semidirect |
| 77. C22×C3×C9 | D8 | semidirect |
| 98. #830 | D9 | semidirect |
| 138. D36 | #67 | semidirect |
| 172. C2×C3⋊C8 | C2×D9 | semidirect |
| 194. C22×C9 | #213 | semidirect |
| 217. C3×C9 | #447 | semidirect |
| 298. C22×C3 | D72 | semidirect |
| 326. C9 | #5217 | semidirect |
| 369. C22 | #88417 | semidirect |
| 375. C3 | #10588414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D36 | 2 |
| #11721819 | 2 |
| C2×#88417 | 2 |
| C9×#830 | 2 |
| #11720283 | 2 |
| #10591162 | 3 |
| #10588414 | 3 |