Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
180 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22549954 | C2 | semidirect |
| 3. #22549953 | C2 | semidirect |
| 4. #22549628 | C2 | semidirect |
| 5. #22549605 | C2 | semidirect |
| 6. C8×C127⋊C8 | C2 | semidirect |
| 7. D4⋊C8×C127 | C2 | semidirect |
| 51. C127⋊C8 | M16 | semidirect |
| 52. C127⋊C8 | D8 | semidirect |
| 84. C127 | #1589 | semidirect |
| 90. D4⋊C8 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523233 | 2 |
| #22549954 | 2 |
| #22549953 | 2 |
| #22549628 | 2 |
| #22549605 | 2 |
| C8×C127⋊C8 | 2 |
| D4⋊C8×C127 | 2 |
| #1589 | 127 |