Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
521 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 521 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #64078⋊C3 | C2 | semidirect |
| 3. C4×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 4. #11720324 | C2 | semidirect |
| 15. #64078 | D3 | semidirect |
| 20. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 165. H(3,𝔽3) | #486 | semidirect |
| 255. C32 | #4694 | semidirect |
| 256. C32 | #5088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721720 | 2 |
| #64078⋊C3 | 2 |
| C4×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #11720324 | 2 |
| #10590277 | 3 |
| #10590273 | 3 |