Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
349 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 51 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×#41⋊C3 | C2 | semidirect |
| 2. C2×C9⋊GL(2,𝔽3) | C2 | semidirect |
| 3. C9⋊#859 | C2 | semidirect |
| 14. C2×C9×#41 | D3 | semidirect |
| 15. C2×#41⋊C9 | D3 | semidirect |
| 27. C9×SL(2,𝔽3) | D4 | semidirect |
| 59. C2×#41⋊C3 | D9 | semidirect |
| 138. C2×#41 | C3⋊D9 | semidirect |
| 163. SL(2,𝔽3) | #611 | semidirect |
| 212. C9 | #5427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41⋊C3 | 2 |
| C2×C9⋊GL(2,𝔽3) | 2 |
| C9⋊#859 | 2 |
| #10593661 | 3 |
| #10589529 | 3 |
| #10588919 | 3 |
| #88536 | 4 |