Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1210 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 272 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. C3×Q8×C22⋊C9 | C2 | semidirect |
| 2. C3×D4×C22⋊C9 | C2 | semidirect |
| 3. C2×C3×C4×C22⋊C9 | C2 | semidirect |
| 5. #41×C22⋊C9 | C3 | direct (N × H) |
| 17. Q8×C22⋊C9 | C2×C3 | semidirect |
| 18. D4×C22⋊C9 | C2×C3 | semidirect |
| 19. C2×C4×C22⋊C9 | C2×C3 | semidirect |
| 25. C22×C3×#41 | C9 | semidirect |
| 51. C3×C22⋊C9 | #41 | direct (N × H) |
| 62. C22×C3×Q8 | C2×C9 | semidirect |
| 64. C22×C3×D4 | C2×C9 | semidirect |
| 66. C23×C3×C4 | C2×C9 | semidirect |
| 94. C22×#41 | C3×C9 | semidirect |
| 111. C3×#41 | C22⋊C9 | direct (N × H) |
| 149. C22⋊C9 | C3×#41 | direct (N × H) |
| 156. C22×Q8 | C2×C3×C9 | semidirect |
| 157. C22×D4 | C2×C3×C9 | semidirect |
| 158. C23×C4 | C2×C3×C9 | semidirect |
| 174. C3×Q8 | C2×C22⋊C9 | semidirect |
| 182. C3×D4 | C2×C22⋊C9 | semidirect |
| 200. C2×C3×C4 | C2×C22⋊C9 | semidirect |
| 216. #41 | C3×C22⋊C9 | direct (N × H) |
| 242. C22×C3 | C9×#41 | semidirect |
| 263. Q8 | C2×C3×C22⋊C9 | semidirect |
| 267. D4 | C2×C3×C22⋊C9 | semidirect |
| 276. C2×C4 | C2×C3×C22⋊C9 | semidirect |
| 294. C22 | C3×C9×#41 | semidirect |
| 300. C3 | #41×C22⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×C22⋊C9 | 2 |
| C3×D4×C22⋊C9 | 2 |
| C2×C3×C4×C22⋊C9 | 2 |
| C22×C32×#41 | 3 |
| #41×C22⋊C9 | 3 |
| C3×C9×#41 | 4 |