Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #22550228 | C2 | semidirect |
| 4. #22550180 | C2 | semidirect |
| 7. #22550086 | C2 | semidirect |
| 8. Q8×C127⋊C8 | C2 | semidirect |
| 9. C4×#14523238 | C2 | semidirect |
| 11. #557×C127 | C2 | semidirect |
| 116. C127 | #3364 | semidirect |
| 117. #557 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550599 | 2 |
| #22550233 | 2 |
| #22550228 | 2 |
| #22550180 | 2 |
| #22550153 | 2 |
| #22550098 | 2 |
| #22550086 | 2 |
| Q8×C127⋊C8 | 2 |
| C4×#14523238 | 2 |
| C4×#14523235 | 2 |
| #557×C127 | 2 |
| #3364 | 127 |