Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
848 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×C22⋊C8×C127 | C2 | semidirect |
| 9. C22×D508 | C4 | semidirect |
| 11. C2×C4⋊Dic127 | C22 | semidirect |
| 16. C22×C8×C127 | C22 | semidirect |
| 56. D508 | C22⋊C4 | semidirect |
| 78. C22×C127 | #102 | semidirect |
| 102. C127 | #1786 | semidirect |
| 105. C2×C22⋊C8 | D127 | semidirect |
| 114. C22×C8 | C2×D127 | semidirect |
| 186. C22 | #16861131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D508 | 2 |
| C2×#16861131 | 2 |
| #22549736 | 2 |
| C2×C22⋊C8×C127 | 2 |
| #1786 | 127 |