Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. #22550285 | C2 | semidirect |
| 3. #22550278 | C2 | semidirect |
| 4. #22550274 | C2 | semidirect |
| 40. M16×C127 | Q8 | semidirect |
| 41. C2×C8×C127 | Q8 | semidirect |
| 76. C127 | #3163 | semidirect |
| 107. M16 | Dic254 | semidirect |
| 108. C2×C8 | Dic254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550504 | 2 |
| #22550285 | 2 |
| #22550278 | 2 |
| #22550274 | 2 |
| #22549918 | 2 |
| #22549914 | 2 |
| C2×#16861141 | 2 |
| #405×C127 | 2 |
| #3163 | 127 |