Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1052 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 188 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×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 3. C32×#830 | C2 | semidirect |
| 4. #11722052 | C2 | semidirect |
| 5. #11722034 | C2 | semidirect |
| 25. C3×#830 | D3 | semidirect |
| 81. #830 | C3⋊D3 | semidirect |
| 175. C33 | #481 | semidirect |
| 257. C32 | #4735 | semidirect |
| 258. C32 | #5034 | semidirect |
| 296. C3 | #10591092 | semidirect |
| 297. C3 | #10592434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C3×#64139 | 2 |
| C32×#830 | 2 |
| #11722052 | 2 |
| #11722034 | 2 |
| #10592434 | 3 |
| #10591092 | 3 |