Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
464 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. C4×C9×SL(2,𝔽3) | C2 | direct (N × H) |
| 4. C2×C4×Q8×C9 | C3 | semidirect |
| 5. C2×C4×Q8⋊C9 | C3 | semidirect |
| 7. C2×C9×SL(2,𝔽3) | C4 | direct (N × H) |
| 14. C4×Q8×C9 | C2×C3 | semidirect |
| 17. C4×Q8⋊C9 | C2×C3 | semidirect |
| 21. C9×SL(2,𝔽3) | C2×C4 | direct (N × H) |
| 23. C2×C4×SL(2,𝔽3) | C9 | direct (N × H) |
| 29. C2×Q8×C9 | C3×C4 | semidirect |
| 35. C2×Q8⋊C9 | C3×C4 | semidirect |
| 52. C4×SL(2,𝔽3) | C2×C9 | direct (N × H) |
| 62. Q8×C9 | C2×C3×C4 | semidirect |
| 71. C2×C4×C9 | SL(2,𝔽3) | direct (N × H) |
| 73. Q8⋊C9 | C2×C3×C4 | semidirect |
| 74. C2×C4×Q8 | C3×C9 | semidirect |
| 87. C2×SL(2,𝔽3) | C4×C9 | direct (N × H) |
| 111. C4×C9 | C2×SL(2,𝔽3) | direct (N × H) |
| 114. C4×Q8 | C2×C3×C9 | semidirect |
| 134. SL(2,𝔽3) | C2×C4×C9 | direct (N × H) |
| 143. C2×C9 | C4×SL(2,𝔽3) | direct (N × H) |
| 149. C2×Q8 | C3×C4×C9 | semidirect |
| 174. C9 | C2×C4×SL(2,𝔽3) | direct (N × H) |
| 179. Q8 | C2×C3×C4×C9 | semidirect |
| 186. C2×C4 | C9×SL(2,𝔽3) | direct (N × H) |
| 204. C4 | C2×C9×SL(2,𝔽3) | direct (N × H) |
| 207. C2 | C4×C9×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 |
|---|---|
| C22×C9×SL(2,𝔽3) | 2 |
| C4×C9×SL(2,𝔽3) | 2 |
| C2×C3×C4×SL(2,𝔽3) | 3 |
| C2×C4×Q8×C9 | 3 |
| C2×C4×Q8⋊C9 | 3 |
| C22×C3×C4×C9 | 4 |