Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
611 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 611 conjugacy classes of subgroups — too many to draw. Only its 132 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×#3745⋊C3 | C2 | semidirect |
| 2. #11721385 | C2 | semidirect |
| 3. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #10592394 | C3 | semidirect |
| 11. C2×#3745 | C2×C3 | semidirect |
| 12. #64083 | C2×C3 | semidirect |
| 16. C32×C4×C8 | D3 | semidirect |
| 17. C32×C4×C8 | C2×C3 | semidirect |
| 23. C8×H(3,𝔽3) | D4 | semidirect |
| 42. C4×H(3,𝔽3) | D8 | semidirect |
| 67. C32×C8 | D12 | semidirect |
| 68. C32×C8 | C3×D4 | semidirect |
| 99. C32×C4 | D24 | semidirect |
| 100. C32×C4 | C3×D8 | semidirect |
| 105. C4×C8 | (C3⋊D3)⋊C3 | semidirect |
| 106. H(3,𝔽3) | #493 | semidirect |
| 160. C32 | #4695 | semidirect |
| 161. C32 | C3×#493 | semidirect |
| 167. C8 | C4⋊((C3⋊D3)⋊C3) | semidirect |
| 182. C4 | #3745⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| #11721385 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #10592394 | 3 |
| C3×#4695 | 3 |