Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1404 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1404 conjugacy classes of subgroups — too many to draw. Only its 236 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. #11723915 | C2 | semidirect |
| 2. C3×#64083 | C2 | semidirect |
| 3. C2×#88791 | C2 | semidirect |
| 4. C32×C4×C3⋊C8 | C2 | semidirect |
| 18. #64083 | D3 | semidirect |
| 22. C3×C4×C3⋊C8 | D3 | semidirect |
| 31. C32×C3⋊C8 | D4 | semidirect |
| 56. C33×C4 | D8 | semidirect |
| 66. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 89. C3×C3⋊C8 | D12 | semidirect |
| 127. C32×C4 | D24 | semidirect |
| 128. C32×C4 | #213 | semidirect |
| 135. C33 | #493 | semidirect |
| 158. C3⋊C8 | C4⋊(C3⋊D3) | semidirect |
| 192. C3×C4 | #3714 | semidirect |
| 193. C3×C4 | #3745 | semidirect |
| 197. C32 | #4695 | semidirect |
| 198. C32 | #5073 | semidirect |
| 224. C4 | #88791 | semidirect |
| 227. C3 | #10590350 | semidirect |
| 228. C3 | #10592394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723915 | 2 |
| C3×#64083 | 2 |
| C2×#88791 | 2 |
| C32×C4×C3⋊C8 | 2 |
| #10592394 | 3 |
| #10590350 | 3 |