Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
990 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 175 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×C4⋊(C3⋊D9) | C2 | semidirect |
| 2. #11721819 | C2 | semidirect |
| 3. C2×#88525 | C2 | semidirect |
| 4. C3×C9×C22⋊C8 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 14. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 15. C2×C3×C8×C9 | C22 | semidirect |
| 17. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 27. C9×C22⋊C8 | D3 | semidirect |
| 43. C4⋊(C3⋊D9) | D4 | semidirect |
| 65. C2×C8×C9 | C2×D3 | semidirect |
| 71. C22×C3×C9 | D8 | semidirect |
| 89. C3×C22⋊C8 | D9 | semidirect |
| 146. C2×C3×C8 | C2×D9 | semidirect |
| 170. C22×C9 | D24 | semidirect |
| 186. C22⋊C8 | C3⋊D9 | semidirect |
| 187. C3×C9 | #447 | semidirect |
| 240. C2×C8 | C2×C3⋊D9 | semidirect |
| 247. C22×C3 | D72 | semidirect |
| 272. C9 | #4732 | semidirect |
| 310. C22 | #88525 | semidirect |
| 315. C3 | #10588414 | 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 |
| #11721819 | 2 |
| C2×#88525 | 2 |
| C3×C9×C22⋊C8 | 2 |
| #11720543 | 2 |
| #10592431 | 3 |
| #10588414 | 3 |