Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
323 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 110 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. C8×C9⋊A4 | C2 | direct (N × H) |
| 4. C23×C8×C9 | C3 | semidirect |
| 5. C2×C8×C22⋊C9 | C3 | semidirect |
| 17. C22×C8×C9 | C2×C3 | semidirect |
| 18. C8×C22⋊C9 | C2×C3 | semidirect |
| 19. C2×C9⋊A4 | C8 | direct (N × H) |
| 45. C2×C8×C9 | A4 | semidirect |
| 47. C9⋊A4 | C2×C8 | direct (N × H) |
| 63. C23×C9 | C3×C8 | semidirect |
| 65. C2×C22⋊C9 | C3×C8 | semidirect |
| 80. C8×C9 | C2×A4 | semidirect |
| 81. C23×C8 | 3−1+2 | semidirect |
| 113. C22×C9 | C2×C3×C8 | semidirect |
| 115. C22⋊C9 | C2×C3×C8 | semidirect |
| 126. C22×C8 | C2×3−1+2 | semidirect |
| 155. C2×C9 | C8×A4 | semidirect |
| 169. C2×C8 | C9⋊A4 | direct (N × H) |
| 189. C9 | C2×C8×A4 | semidirect |
| 193. C23 | C8×3−1+2 | semidirect |
| 205. C8 | C2×C9⋊A4 | direct (N × H) |
| 220. C22 | C2×C8×3−1+2 | semidirect |
| 231. C2 | C8×C9⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9⋊A4 | 2 |
| C8×C9⋊A4 | 2 |
| C2×C3×C8×A4 | 3 |
| C23×C8×C9 | 3 |
| C2×C8×C22⋊C9 | 3 |
| C2×C8×3−1+2 | 4 |