Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
700 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 173 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. C4×C4⋊(C3⋊D9) | C2 | semidirect |
| 4. C3×C9×C4⋊C8 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 26. C9×C4⋊C8 | D3 | semidirect |
| 39. C4⋊(C3⋊D9) | D4 | semidirect |
| 72. C3×C4×C9 | D8 | semidirect |
| 82. C3×C4⋊C8 | D9 | semidirect |
| 160. C4×C9 | D24 | semidirect |
| 167. C4⋊C8 | C3⋊D9 | semidirect |
| 169. C3×C9 | #459 | semidirect |
| 234. C3×C4 | D72 | semidirect |
| 243. C9 | #4843 | semidirect |
| 277. C4 | #88525 | semidirect |
| 280. C3 | #10588527 | 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 |
| C4×C4⋊(C3⋊D9) | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720543 | 2 |
| #10592542 | 3 |
| #10588527 | 3 |