Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22550642 | C2 | semidirect |
| 3. #22549892 | C2 | semidirect |
| 4. #22549882 | C2 | semidirect |
| 5. C2×#16861125 | C2 | semidirect |
| 6. #22549647 | C2 | semidirect |
| 7. #338×C127 | C2 | semidirect |
| 12. C2×#14523237 | C4 | semidirect |
| 13. C2×D1016 | C4 | semidirect |
| 113. C127 | #1903 | semidirect |
| 120. #338 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861237 | 2 |
| #22550642 | 2 |
| #22549892 | 2 |
| #22549882 | 2 |
| C2×#16861125 | 2 |
| #22549647 | 2 |
| #338×C127 | 2 |
| #1903 | 127 |