Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
852 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 229 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. C32×C4×C4⋊C4 | C2 | semidirect |
| 3. #10592624 | C2 | semidirect |
| 4. #10589317 | C2 | semidirect |
| 13. #64083 | C4 | semidirect |
| 15. C4×C4⋊(C3⋊D3) | C4 | semidirect |
| 16. #64078 | C4 | semidirect |
| 22. C3×C4×C4⋊C4 | D3 | semidirect |
| 90. C4×C4⋊C4 | C3⋊D3 | semidirect |
| 215. C32 | #1502 | semidirect |
| 262. C3 | #69469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| C32×C4×C4⋊C4 | 2 |
| #10592624 | 2 |
| #10589317 | 2 |
| #69469 | 3 |