Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
808 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 113 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. D3×#41⋊C9 | C2 | semidirect |
| 3. C3⋊#63700 | C2 | semidirect |
| 7. C3×#41⋊C9 | C22 | semidirect |
| 8. D3×Q8⋊C9 | C22 | semidirect |
| 9. C3⋊(#41⋊C9) | C22 | semidirect |
| 19. #63700 | D3 | direct (N × H) |
| 24. C3×Q8⋊C9 | C23 | semidirect |
| 26. D3×H(5,𝔽2) | C9 | semidirect |
| 49. #41⋊C9 | C2×D3 | semidirect |
| 58. C3×H(5,𝔽2) | C2×C9 | semidirect |
| 64. #1009 | C2×C9 | semidirect |
| 94. Q8⋊C9 | C22×D3 | semidirect |
| 156. H(5,𝔽2) | D3×C9 | semidirect |
| 289. D3 | #63700 | direct (N × H) |
| 301. C3 | C2×#63700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63700 | 2 |
| D3×#41⋊C9 | 2 |
| C3⋊#63700 | 2 |
| C3×D3×H(5,𝔽2) | 3 |
| C2×#63700 | 3 |
| D3×Q8×C9 | 4 |