Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22550184 | C2 | semidirect |
| 4. #22550172 | C2 | semidirect |
| 5. #22550162 | C2 | semidirect |
| 37. C2×Dic254 | Q8 | semidirect |
| 107. C127 | #3078 | 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 |
| #22550184 | 2 |
| #22550172 | 2 |
| #22550162 | 2 |
| #22549918 | 2 |
| #22549886 | 2 |
| #423×C127 | 2 |
| #3078 | 127 |