Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. #22550162 | C2 | semidirect |
| 5. #22550087 | C2 | semidirect |
| 7. #22549984 | C2 | semidirect |
| 104. C127 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550433 | 2 |
| C2×C4×Dic254 | 2 |
| #22550207 | 2 |
| #22550162 | 2 |
| #22550087 | 2 |
| #22550034 | 2 |
| #22549984 | 2 |
| #432×C127 | 2 |
| #3113 | 127 |