Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
460 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#88414 | C2 | semidirect |
| 3. C4×C9×C3⋊C8 | C2 | semidirect |
| 4. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 5. #11720282 | C2 | semidirect |
| 27. C4⋊(C9⋊C8) | D3 | semidirect |
| 37. C9×C3⋊C8 | D4 | semidirect |
| 69. C3×C4×C9 | M16 | semidirect |
| 83. C4×C3⋊C8 | D9 | semidirect |
| 164. C4×C9 | ΓL(1,𝔽25) | semidirect |
| 174. C3×C9 | #436 | semidirect |
| 204. C3⋊C8 | D36 | semidirect |
| 244. C3×C4 | #3663 | semidirect |
| 255. C9 | #4838 | semidirect |
| 285. C4 | #88414 | semidirect |
| 289. C3 | #10588370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D9) | 2 |
| C2×#88414 | 2 |
| C4×C9×C3⋊C8 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720282 | 2 |
| #10590338 | 3 |
| #10588370 | 3 |