Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1296 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 172 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. C32×#875 | C2 | semidirect |
| 3. C2×#88795 | C2 | semidirect |
| 4. C2×#88790 | C2 | semidirect |
| 5. C3×#63630 | C2 | semidirect |
| 23. C3×#875 | D3 | semidirect |
| 26. #63630 | D3 | semidirect |
| 38. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 75. #875 | C3⋊D3 | semidirect |
| 107. C3⋊(C3⋊C8) | D12 | semidirect |
| 161. C33 | #496 | semidirect |
| 232. C32 | #4712 | semidirect |
| 233. C32 | #5058 | semidirect |
| 265. C3 | #10590351 | semidirect |
| 266. C3 | #10592757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723915 | 2 |
| C32×#875 | 2 |
| C2×#88795 | 2 |
| C2×#88790 | 2 |
| C3×#63630 | 2 |
| #10592757 | 3 |
| #10590351 | 3 |