Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22549930 | C2 | semidirect |
| 3. #22549926 | C2 | semidirect |
| 4. #22549899 | C2 | semidirect |
| 6. M16×Dic127 | C2 | semidirect |
| 17. Dic127⋊C8 | C22 | semidirect |
| 19. #16861119 | C22 | semidirect |
| 20. C8×Dic127 | C22 | semidirect |
| 56. C2×Dic127 | M16 | semidirect |
| 93. C127 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic127 | 2 |
| #22549930 | 2 |
| #22549926 | 2 |
| #22549899 | 2 |
| #22549840 | 2 |
| M16×Dic127 | 2 |
| #407×C127 | 2 |
| #2920 | 127 |