Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
530 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 530 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×D72 | C2 | semidirect |
| 2. C3×#63436 | C2 | semidirect |
| 3. C3×C4×C8×C9 | C2 | semidirect |
| 5. #10588377 | C3 | direct (N × H) |
| 14. C2×D72 | C2×C3 | semidirect |
| 15. #63436 | C2×C3 | semidirect |
| 17. C4×C8×C9 | C2×C3 | semidirect |
| 23. C3×C8×C9 | D4 | semidirect |
| 41. C3×C4×C9 | D8 | semidirect |
| 48. C3×C4×C8 | D9 | semidirect |
| 64. C8×C9 | C3×D4 | semidirect |
| 92. C4×C9 | C3×D8 | semidirect |
| 96. C4×C8 | C3×D9 | semidirect |
| 97. C3×C9 | #493 | semidirect |
| 111. C3×C8 | D36 | semidirect |
| 135. C3×C4 | D72 | semidirect |
| 141. C9 | C3×#493 | semidirect |
| 147. C8 | C3×D36 | semidirect |
| 159. C4 | C3×D72 | semidirect |
| 162. C3 | #10588377 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| C3×#63436 | 2 |
| C3×C4×C8×C9 | 2 |
| C3×#4695 | 3 |
| #10588377 | 3 |