Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #22550604 | C2 | semidirect |
| 3. #22550226 | C2 | semidirect |
| 4. #22550183 | C2 | semidirect |
| 7. #22550083 | C2 | semidirect |
| 8. Q8×C127⋊C8 | C2 | semidirect |
| 9. C4×#14523238 | C2 | semidirect |
| 116. C127 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550604 | 2 |
| #22550230 | 2 |
| #22550226 | 2 |
| #22550183 | 2 |
| #22550156 | 2 |
| #22550095 | 2 |
| #22550083 | 2 |
| Q8×C127⋊C8 | 2 |
| C4×#14523238 | 2 |
| C4×#14523236 | 2 |
| #556×C127 | 2 |
| #3364 | 127 |