Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
416 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 103 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×#88414 | C2 | semidirect |
| 4. #11720542 | C2 | semidirect |
| 5. C3×Dic9⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 36. Dic9⋊C8 | D3 | semidirect |
| 52. C9×C3⋊C8 | D4 | semidirect |
| 97. C3×Dic9 | M16 | semidirect |
| 102. C2×ΓL(1,𝔽25) | D9 | semidirect |
| 219. Dic9 | ΓL(1,𝔽25) | semidirect |
| 227. C3×C9 | #436 | semidirect |
| 266. C3⋊C8 | #611 | semidirect |
| 329. C9 | #4838 | semidirect |
| 374. 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×#6195 | 2 |
| C2×#88414 | 2 |
| #11720542 | 2 |
| C3×Dic9⋊C8 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| C3⋊C8×Dic9 | 2 |
| #10590731 | 3 |
| #10588810 | 3 |