Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 3. #22550182 | C2 | semidirect |
| 4. #22550181 | C2 | semidirect |
| 5. #22550168 | C2 | semidirect |
| 6. #22550162 | C2 | semidirect |
| 7. #22550161 | C2 | semidirect |
| 11. #477×C127 | C2 | semidirect |
| 47. Q8×D127 | Q8 | semidirect |
| 131. C127 | #3078 | semidirect |
| 137. #477 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550431 | 2 |
| C4×Q8×D127 | 2 |
| #22550182 | 2 |
| #22550181 | 2 |
| #22550168 | 2 |
| #22550162 | 2 |
| #22550161 | 2 |
| #22549917 | 2 |
| #22549898 | 2 |
| #22549883 | 2 |
| #477×C127 | 2 |
| #3078 | 127 |