Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
224 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×C16×H(3,𝔽3) | C2 | semidirect |
| 3. #63639⋊C3 | C2 | semidirect |
| 4. #10589374 | C3 | semidirect |
| 16. C2×C32×C16 | D3 | semidirect |
| 17. C2×C32×C16 | C2×C3 | semidirect |
| 18. #63639 | C2×C3 | semidirect |
| 123. C2×C16 | (C3⋊D3)⋊C3 | semidirect |
| 124. H(3,𝔽3) | #350 | semidirect |
| 186. C32 | #4508 | semidirect |
| 187. C32 | C3×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64110⋊C3 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| #63639⋊C3 | 2 |
| #10589374 | 3 |
| C3×#4508 | 3 |