Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
288 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 30 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. #11724155 | C2 | direct (N × H) |
| 4. C2×C32×SL(2,𝔽3) | C4 | semidirect |
| 6. C3⋊(C3⋊(#41⋊C3)) | C4 | semidirect |
| 15. C32×SL(2,𝔽3) | C2×C4 | semidirect |
| 72. C2×SL(2,𝔽3) | #157 | semidirect |
| 107. SL(2,𝔽3) | C2×#157 | semidirect |
| 113. C2×C32 | GU(2,𝔽3) | semidirect |
| 144. C32 | C2×GU(2,𝔽3) | semidirect |
| 182. C2 | #11724155 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊(#41⋊C3)) | 2 |
| #11724155 | 2 |
| C2×#63785 | 3 |
| C2×C3⋊#622 | 4 |
| C2×GU(2,𝔽3) | 9 |