Finite Group DatabasebetaFinite Group Databasebeta← C2×C9×C22⋊SL(2,𝔽3) #13164868
Order 1728.
605 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 74 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. C9×C22⋊SL(2,𝔽3) | C2 | direct (N × H) |
| 3. C23×Q8×C9 | C3 | semidirect |
| 4. C2×C22⋊(Q8⋊C9) | C3 | semidirect |
| 11. C22×Q8×C9 | C2×C3 | semidirect |
| 13. C22⋊(Q8⋊C9) | C2×C3 | semidirect |
| 18. C2×C22⋊SL(2,𝔽3) | C9 | direct (N × H) |
| 28. C2×Q8×C9 | A4 | semidirect |
| 41. C22⋊SL(2,𝔽3) | C2×C9 | direct (N × H) |
| 48. C23×C9 | SL(2,𝔽3) | semidirect |
| 55. Q8×C9 | C2×A4 | semidirect |
| 61. C23×Q8 | C3×C9 | semidirect |
| 87. C22×C9 | C2×SL(2,𝔽3) | semidirect |
| 95. C22×Q8 | C2×C3×C9 | semidirect |
| 121. C2×C9 | C22⋊SL(2,𝔽3) | direct (N × H) |
| 129. C2×Q8 | C9×A4 | semidirect |
| 149. C9 | C2×C22⋊SL(2,𝔽3) | direct (N × H) |
| 153. C23 | C9×SL(2,𝔽3) | semidirect |
| 158. Q8 | C2×C9×A4 | semidirect |
| 177. C22 | C2×C9×SL(2,𝔽3) | semidirect |
| 186. C2 | C9×C22⋊SL(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C22⋊SL(2,𝔽3) | 2 |
| C2×C3×C22⋊SL(2,𝔽3) | 3 |
| C23×Q8×C9 | 3 |
| C2×C22⋊(Q8⋊C9) | 3 |
| C22×C9×A4 | 4 |
| C2×C9×SL(2,𝔽3) | 4 |