Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #22549772 | C2 | semidirect |
| 4. #22549767 | C2 | semidirect |
| 5. #22549738 | C2 | semidirect |
| 6. #22549735 | C2 | semidirect |
| 7. #22549722 | C2 | semidirect |
| 8. C4×C4⋊C4×C127 | C2 | semidirect |
| 11. C4×D508 | C4 | semidirect |
| 97. C127 | #2319 | semidirect |
| 104. C4×C4⋊C4 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D508 | 2 |
| #22549777 | 2 |
| #22549772 | 2 |
| #22549767 | 2 |
| #22549738 | 2 |
| #22549735 | 2 |
| #22549722 | 2 |
| C4×C4⋊C4×C127 | 2 |
| #2319 | 127 |