Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 154 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. C2×C3×#3664 | C2 | semidirect |
| 3. C3×#63431 | C2 | semidirect |
| 4. C3×C4×C8×C9 | C2 | semidirect |
| 6. #10588375 | C3 | direct (N × H) |
| 18. C2×#3664 | C2×C3 | semidirect |
| 20. #63431 | C2×C3 | semidirect |
| 22. C4×C8×C9 | C2×C3 | semidirect |
| 30. C3×C8×C9 | D4 | semidirect |
| 52. C3×C4×C9 | SD16 | semidirect |
| 62. C3×C4×C8 | D9 | semidirect |
| 82. C8×C9 | C3×D4 | semidirect |
| 115. C4×C9 | C3×SD16 | semidirect |
| 121. C4×C8 | C3×D9 | semidirect |
| 122. C3×C9 | #492 | semidirect |
| 140. C3×C8 | D36 | semidirect |
| 167. C3×C4 | #3664 | semidirect |
| 174. C9 | C3×#492 | semidirect |
| 182. C8 | C3×D36 | semidirect |
| 195. C4 | C3×#3664 | semidirect |
| 198. C3 | #10588375 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3664 | 2 |
| C3×#63436 | 2 |
| C3×#63431 | 2 |
| C3×C4×C8×C9 | 2 |
| C3×#4693 | 3 |
| #10588375 | 3 |