Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22549929 | C2 | semidirect |
| 3. #22549605 | C2 | semidirect |
| 4. #431×C127 | C2 | semidirect |
| 13. C4⋊(C127⋊C8) | C22 | semidirect |
| 19. C4×C8×C127 | C22 | semidirect |
| 23. C2×D508 | C8 | semidirect |
| 88. C127 | #1478 | semidirect |
| 91. #431 | D127 | semidirect |
| 107. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D508 | 2 |
| #22549929 | 2 |
| #22549605 | 2 |
| #431×C127 | 2 |
| #1478 | 127 |