Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#16861207 | C2 | semidirect |
| 5. #22550085 | C2 | semidirect |
| 6. #22550080 | C2 | semidirect |
| 7. #22549899 | C2 | semidirect |
| 8. #22549884 | C2 | semidirect |
| 9. #419×C127 | C2 | semidirect |
| 116. Dic127 | #137 | semidirect |
| 122. C127 | #3039 | semidirect |
| 131. #419 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861242 | 2 |
| C2×#16861240 | 2 |
| C2×#16861207 | 2 |
| #22550344 | 2 |
| #22550085 | 2 |
| #22550080 | 2 |
| #22549899 | 2 |
| #22549884 | 2 |
| #419×C127 | 2 |
| #3039 | 127 |