Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
610 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 181 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×#88523 | C2 | semidirect |
| 3. C3×C9×C4⋊C8 | C2 | semidirect |
| 4. #11720542 | C2 | semidirect |
| 5. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 24. C9×C4⋊C8 | D3 | semidirect |
| 37. C3⋊(C9⋊C8) | D4 | semidirect |
| 63. C3×C4×C9 | M16 | semidirect |
| 71. C3×C4⋊C8 | D9 | semidirect |
| 136. C4×C9 | ΓL(1,𝔽25) | semidirect |
| 142. C4⋊C8 | C3⋊D9 | semidirect |
| 145. C3×C9 | #436 | semidirect |
| 195. C3×C4 | #3663 | semidirect |
| 204. C9 | #4838 | semidirect |
| 230. C4 | #88523 | semidirect |
| 233. C3 | #10588522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88523 | 2 |
| C4×C4⋊(C3⋊D9) | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720542 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10592537 | 3 |
| #10588522 | 3 |