Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22550180 | C2 | semidirect |
| 3. #22550173 | C2 | semidirect |
| 4. #22550168 | C2 | semidirect |
| 5. #22550153 | C2 | semidirect |
| 6. #22549919 | C2 | semidirect |
| 7. C2×#16861142 | C2 | semidirect |
| 8. #22549903 | C2 | semidirect |
| 11. #544×C127 | C2 | semidirect |
| 42. #14523248 | Q8 | semidirect |
| 124. C127 | #3083 | semidirect |
| 125. #544 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550356 | 2 |
| #22550180 | 2 |
| #22550173 | 2 |
| #22550168 | 2 |
| #22550153 | 2 |
| #22549919 | 2 |
| C2×#16861142 | 2 |
| #22549903 | 2 |
| #22549875 | 2 |
| #22549870 | 2 |
| #544×C127 | 2 |
| #3083 | 127 |