Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #22550431 | C2 | semidirect |
| 3. #22550181 | C2 | semidirect |
| 4. #22550175 | C2 | semidirect |
| 5. #22550171 | C2 | semidirect |
| 6. #22550167 | C2 | semidirect |
| 7. #22550153 | C2 | semidirect |
| 8. #22549911 | C2 | semidirect |
| 9. C4⋊C8×D127 | C2 | semidirect |
| 11. #475×C127 | C2 | semidirect |
| 44. #14523249 | Q8 | semidirect |
| 135. C127 | #3076 | semidirect |
| 142. #475 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550431 | 2 |
| C4×#14523249 | 2 |
| #22550181 | 2 |
| #22550175 | 2 |
| #22550171 | 2 |
| #22550167 | 2 |
| #22550153 | 2 |
| #22549911 | 2 |
| C4⋊C8×D127 | 2 |
| #22549871 | 2 |
| #475×C127 | 2 |
| #3076 | 127 |