Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
404 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 101 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×C9×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×#88413 | C2 | semidirect |
| 4. #11720537 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 7. #11720271 | C2 | semidirect |
| 34. (C2×D9)⋊C8 | D3 | semidirect |
| 52. C9×C3⋊C8 | D4 | semidirect |
| 95. C3⋊Dic9 | M16 | semidirect |
| 103. C2×ΓL(1,𝔽25) | D9 | semidirect |
| 223. C3×C9 | #436 | semidirect |
| 260. C3⋊C8 | #611 | semidirect |
| 320. C9 | #4729 | semidirect |
| 364. C3 | #10588810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×ΓL(1,𝔽25) | 2 |
| C4×#6194 | 2 |
| C2×#88413 | 2 |
| #11720537 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720271 | 2 |
| #10590735 | 3 |
| #10588810 | 3 |