Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1178 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 274 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 | direct (N × H) |
| 2. C2×C3×#41⋊C9 | C2 | semidirect |
| 4. C2×#63700 | C3 | direct (N × H) |
| 6. C3×#41⋊C9 | C22 | semidirect |
| 7. C2×C3×Q8⋊C9 | C22 | semidirect |
| 13. #63700 | C2×C3 | direct (N × H) |
| 14. C2×#41⋊C9 | C2×C3 | semidirect |
| 17. C3×Q8⋊C9 | C23 | semidirect |
| 18. C2×C3×H(5,𝔽2) | C9 | semidirect |
| 33. #41⋊C9 | C22×C3 | semidirect |
| 34. C2×Q8⋊C9 | C22×C3 | semidirect |
| 39. C3×H(5,𝔽2) | C2×C9 | semidirect |
| 62. Q8⋊C9 | C23×C3 | semidirect |
| 63. C2×H(5,𝔽2) | C3×C9 | semidirect |
| 100. H(5,𝔽2) | C2×C3×C9 | semidirect |
| 179. C2×C3 | #63700 | direct (N × H) |
| 190. C3 | C2×#63700 | direct (N × H) |
| 193. C2 | C3×#63700 | 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 |
| C2×C3×#41⋊C9 | 2 |
| C2×C32×H(5,𝔽2) | 3 |
| C2×#63700 | 3 |
| C2×C3×Q8×C9 | 4 |