Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1851 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 1851 conjugacy classes of subgroups — too many to draw. Only its 215 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. C2×#88654 | C2 | semidirect |
| 2. #11721720 | C2 | semidirect |
| 3. #11721385 | C2 | semidirect |
| 4. C42×(C3⋊D3)⋊C3 | C2 | semidirect |
| 5. #11721158 | C2 | semidirect |
| 9. C2×C4⋊#272 | C22 | semidirect |
| 10. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 12. C2×#6200 | C22 | semidirect |
| 14. C42×H(3,𝔽3) | C22 | semidirect |
| 15. C4×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 18. #64083 | D3 | semidirect |
| 19. C42×C3⋊D3 | D3 | semidirect |
| 35. C4×(C3⋊D3)⋊C3 | D4 | semidirect |
| 42. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 54. C32×C42 | C2×D3 | semidirect |
| 55. C32×C42 | C2×D3 | semidirect |
| 56. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 63. C4×H(3,𝔽3) | C2×D4 | semidirect |
| 64. (C3⋊Dic3)⋊C3 | C2×D4 | semidirect |
| 95. C4×C3⋊D3 | D12 | semidirect |
| 108. (C3⋊D3)⋊C3 | #127 | semidirect |
| 148. C32×C4 | C2×D12 | semidirect |
| 149. C32×C4 | D3×D4 | semidirect |
| 150. C3⋊Dic3 | C2×D12 | semidirect |
| 157. H(3,𝔽3) | C2×#127 | semidirect |
| 195. C3⋊D3 | #874 | semidirect |
| 208. C42 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 234. C32 | C2×#874 | semidirect |
| 235. C32 | D3×#127 | semidirect |
| 266. C4 | #88654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88654 | 2 |
| #11721720 | 2 |
| #11721385 | 2 |
| C42×(C3⋊D3)⋊C3 | 2 |
| #11721158 | 2 |
| #10594008 | 3 |
| D3×#874 | 3 |