Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22550233 | C2 | semidirect |
| 3. #22550228 | C2 | semidirect |
| 4. #22550224 | C2 | semidirect |
| 5. #22549870 | C2 | semidirect |
| 6. C2×C4×C127⋊C8 | C2 | semidirect |
| 7. #533×C127 | C2 | semidirect |
| 79. C127 | #3131 | semidirect |
| 80. #533 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550426 | 2 |
| #22550233 | 2 |
| #22550228 | 2 |
| #22550224 | 2 |
| #22549870 | 2 |
| C2×C4×C127⋊C8 | 2 |
| #533×C127 | 2 |
| #3131 | 127 |