Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D127 | C2 | semidirect |
| 4. #22550086 | C2 | semidirect |
| 5. #22550084 | C2 | semidirect |
| 6. #22550082 | C2 | semidirect |
| 7. #22550080 | C2 | semidirect |
| 8. #22550078 | C2 | semidirect |
| 9. #22549898 | C2 | semidirect |
| 10. #22549883 | C2 | semidirect |
| 11. #462×C127 | C2 | semidirect |
| 132. C4×C127 | #137 | semidirect |
| 139. Dic127 | #137 | semidirect |
| 146. C127 | #3039 | semidirect |
| 152. #462 | D127 | semidirect |
| 283. C4 | #16861241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861241 | 2 |
| C4⋊Q8×D127 | 2 |
| C4×#14523249 | 2 |
| #22550086 | 2 |
| #22550084 | 2 |
| #22550082 | 2 |
| #22550080 | 2 |
| #22550078 | 2 |
| #22549898 | 2 |
| #22549883 | 2 |
| #462×C127 | 2 |
| #3039 | 127 |