Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
746 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 193 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×#88683 | C2 | direct (N × H) |
| 2. C22×C9⋊SL(2,𝔽3) | C2 | semidirect |
| 4. C22×C9×#41 | C3 | semidirect |
| 5. C22×#41⋊C9 | C3 | semidirect |
| 7. #88683 | C22 | direct (N × H) |
| 8. C2×C9⋊SL(2,𝔽3) | C22 | semidirect |
| 12. C2×C9×#41 | C2×C3 | semidirect |
| 16. C2×#41⋊C9 | C2×C3 | semidirect |
| 20. C9⋊SL(2,𝔽3) | C23 | semidirect |
| 29. C9×#41 | C22×C3 | semidirect |
| 39. #41⋊C9 | C22×C3 | semidirect |
| 70. C22×#41 | 3−1+2 | semidirect |
| 95. C22×C9 | #41⋊C3 | semidirect |
| 102. C2×#41 | C2×3−1+2 | semidirect |
| 128. C2×C9 | C2×#41⋊C3 | semidirect |
| 133. #41 | C22×3−1+2 | semidirect |
| 154. C9 | C22×#41⋊C3 | semidirect |
| 175. C22 | #88683 | direct (N × H) |
| 183. C2 | C2×#88683 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88683 | 2 |
| C22×C9⋊SL(2,𝔽3) | 2 |
| C22×C3×#41⋊C3 | 3 |
| C22×C9×#41 | 3 |
| C22×#41⋊C9 | 3 |
| C22×C4×3−1+2 | 4 |