Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 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. #22550228 | C2 | semidirect |
| 4. #22550225 | C2 | semidirect |
| 5. #22550160 | C2 | semidirect |
| 8. #22550000 | C2 | semidirect |
| 11. #475×C127 | C2 | semidirect |
| 78. Dic254 | SD16 | semidirect |
| 119. C127 | #3359 | semidirect |
| 125. #475 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550604 | 2 |
| #22550541 | 2 |
| #22550228 | 2 |
| #22550225 | 2 |
| #22550160 | 2 |
| #22550082 | 2 |
| #22550080 | 2 |
| #22550000 | 2 |
| C4×#14523235 | 2 |
| #22549963 | 2 |
| #475×C127 | 2 |
| #3359 | 127 |