Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#16861242 | C2 | semidirect |
| 2. C2×#16861217 | C2 | semidirect |
| 4. #22550452 | C2 | semidirect |
| 5. #22550135 | C2 | semidirect |
| 6. #22550123 | C2 | semidirect |
| 7. #22550118 | C2 | semidirect |
| 8. #22550106 | C2 | semidirect |
| 9. #22549870 | C2 | semidirect |
| 10. C2×#16861132 | C2 | semidirect |
| 11. #428×C127 | C2 | semidirect |
| 77. M16×C127 | D4 | semidirect |
| 144. C127 | #3063 | semidirect |
| 153. #428 | D127 | semidirect |
| 210. M16 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861242 | 2 |
| C2×#16861217 | 2 |
| #22550457 | 2 |
| #22550452 | 2 |
| #22550135 | 2 |
| #22550123 | 2 |
| #22550118 | 2 |
| #22550106 | 2 |
| #22549870 | 2 |
| C2×#16861132 | 2 |
| #428×C127 | 2 |
| #3063 | 127 |