Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#16861135 | C2 | semidirect |
| 3. #22549875 | C2 | semidirect |
| 4. C2×#16861125 | C2 | semidirect |
| 5. #22549777 | C2 | semidirect |
| 6. #22549635 | C2 | semidirect |
| 7. #428×C127 | C2 | semidirect |
| 56. M16×C127 | D4 | semidirect |
| 131. C127 | #2037 | semidirect |
| 133. #428 | D127 | semidirect |
| 181. M16 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550445 | 2 |
| C2×#16861135 | 2 |
| #22549875 | 2 |
| C2×#16861125 | 2 |
| #22549777 | 2 |
| #22549635 | 2 |
| #428×C127 | 2 |
| #2037 | 127 |