Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
432 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16861131 | C2 | semidirect |
| 3. #22549736 | C2 | semidirect |
| 4. #22549639 | C2 | semidirect |
| 5. C23×C8×C127 | C2 | semidirect |
| 9. #16861183 | C4 | semidirect |
| 46. C2×C8×C127 | D4 | semidirect |
| 82. C22×C127 | #102 | semidirect |
| 107. C127 | #1893 | semidirect |
| 108. C23×C8 | D127 | semidirect |
| 147. C2×C8 | C22⋊D127 | semidirect |
| 194. C22 | #16861131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861183 | 2 |
| C2×#16861131 | 2 |
| #22549736 | 2 |
| #22549639 | 2 |
| C23×C8×C127 | 2 |
| #1893 | 127 |