Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
322 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 40 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. C3×#63700 | C2 | semidirect |
| 2. C3×#63692 | C2 | semidirect |
| 3. C3×#63422 | C2 | semidirect |
| 5. #10589531 | C3 | direct (N × H) |
| 15. #63700 | C2×C3 | semidirect |
| 16. #63692 | C2×C3 | semidirect |
| 20. #63422 | C2×C3 | semidirect |
| 23. C3×Q8⋊C9 | D4 | semidirect |
| 51. C3×H(5,𝔽2) | D9 | semidirect |
| 85. Q8⋊C9 | C3×D4 | semidirect |
| 137. H(5,𝔽2) | C3×D9 | semidirect |
| 271. C3 | #10589531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63700 | 2 |
| C3×#63692 | 2 |
| C3×#63422 | 2 |
| C3×#5241 | 3 |
| #10589531 | 3 |
| C3×#3675 | 4 |