Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22549914 | C2 | semidirect |
| 3. #22549704 | C2 | semidirect |
| 4. #22549702 | C2 | semidirect |
| 5. #22549678 | C2 | semidirect |
| 6. #22549678 | C2 | semidirect |
| 7. C22⋊C16×C127 | C2 | semidirect |
| 70. C127 | #2234 | semidirect |
| 77. C22⋊C16 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550112 | 2 |
| #22549914 | 2 |
| #22549704 | 2 |
| #22549702 | 2 |
| #22549678 | 2 |
| C22⋊C16×C127 | 2 |
| #2234 | 127 |