Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
810 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 231 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×#88525 | C2 | semidirect |
| 2. #11721711 | C2 | semidirect |
| 3. C3×C4×C8×C9 | C2 | semidirect |
| 16. C4×C8×C9 | D3 | semidirect |
| 22. C3×C8×C9 | D4 | semidirect |
| 38. C3×C4×C9 | D8 | semidirect |
| 44. C3×C4×C8 | D9 | semidirect |
| 57. C8×C9 | D12 | semidirect |
| 80. C4×C9 | D24 | semidirect |
| 84. C4×C8 | C3⋊D9 | semidirect |
| 85. C3×C9 | #493 | semidirect |
| 96. C3×C8 | D36 | semidirect |
| 115. C3×C4 | D72 | semidirect |
| 120. C9 | #4695 | semidirect |
| 126. C8 | C4⋊(C3⋊D9) | semidirect |
| 136. C4 | #88525 | semidirect |
| 138. C3 | #10588377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| #11721711 | 2 |
| C3×C4×C8×C9 | 2 |
| #10592394 | 3 |
| #10588377 | 3 |