Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
920 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 149 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. C4×C4⋊#272 | C2 | semidirect |
| 2. C4×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. #64078⋊C3 | C2 | semidirect |
| 4. #11721159 | C2 | semidirect |
| 5. #11721156 | C2 | semidirect |
| 6. #11721155 | C2 | semidirect |
| 7. #11721089 | C2 | semidirect |
| 8. #11721081 | C2 | semidirect |
| 27. C4×C4⋊(C3⋊D3) | D3 | semidirect |
| 28. #64078 | D3 | semidirect |
| 272. H(3,𝔽3) | #555 | semidirect |
| 400. C32 | #5563 | semidirect |
| 401. C32 | #5734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#272 | 2 |
| C4×C4⋊((C3⋊D3)⋊C3) | 2 |
| #64078⋊C3 | 2 |
| #11721159 | 2 |
| #11721156 | 2 |
| #11721155 | 2 |
| #11721089 | 2 |
| #11721081 | 2 |
| #10593988 | 3 |
| #10593987 | 3 |