Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22549914 | C2 | semidirect |
| 4. #22549632 | C2 | semidirect |
| 5. #427×C127 | C2 | semidirect |
| 12. C2×#14523231 | C4 | semidirect |
| 13. C2×C8×D127 | C4 | semidirect |
| 93. C127 | #1812 | semidirect |
| 96. #427 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861215 | 2 |
| #22549914 | 2 |
| #22549849 | 2 |
| #22549632 | 2 |
| #427×C127 | 2 |
| #1812 | 127 |