Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
142 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22550281 | C2 | semidirect |
| 3. #22549702 | C2 | semidirect |
| 5. C4⋊C16×C127 | C2 | semidirect |
| 19. D1016 | Q8 | semidirect |
| 56. C127 | #2224 | semidirect |
| 60. C4⋊C16 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550281 | 2 |
| C4×D1016 | 2 |
| #22549702 | 2 |
| #22549678 | 2 |
| C4⋊C16×C127 | 2 |
| #2224 | 127 |