Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 5. #22550159 | C2 | semidirect |
| 6. #22550084 | C2 | semidirect |
| 8. #22549983 | C2 | semidirect |
| 9. #22549980 | C2 | semidirect |
| 128. C127 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550428 | 2 |
| C2×Q8×Dic127 | 2 |
| #22550207 | 2 |
| #22550204 | 2 |
| #22550159 | 2 |
| #22550084 | 2 |
| #22550032 | 2 |
| #22549983 | 2 |
| #22549980 | 2 |
| #22549930 | 2 |
| #451×C127 | 2 |
| #3113 | 127 |