Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
990 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 211 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×D4×C9 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. #11721819 | C2 | semidirect |
| 4. #11720576 | C2 | semidirect |
| 5. #11720571 | C2 | semidirect |
| 14. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 17. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 18. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 22. C22×D4×C9 | D3 | semidirect |
| 37. C3×D4×C9 | D4 | semidirect |
| 75. C22×C3×C9 | D8 | semidirect |
| 83. C22×C3×D4 | D9 | semidirect |
| 117. D4×C9 | #67 | semidirect |
| 174. C22×C9 | #213 | semidirect |
| 182. C22×D4 | C3⋊D9 | semidirect |
| 187. C3×C9 | #447 | semidirect |
| 204. C3×D4 | #611 | semidirect |
| 255. C22×C3 | #3673 | semidirect |
| 272. C9 | #5217 | semidirect |
| 283. D4 | #6233 | semidirect |
| 310. C22 | #88544 | semidirect |
| 315. C3 | #10588898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4×C9 | 2 |
| C2×#88544 | 2 |
| #11721819 | 2 |
| #11720576 | 2 |
| #11720571 | 2 |
| #10592916 | 3 |
| #10588898 | 3 |