Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
252 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#16861145 | C2 | semidirect |
| 4. C127⋊#338 | C2 | semidirect |
| 5. C2×#108×C127 | C2 | semidirect |
| 82. C127 | #1813 | semidirect |
| 85. C2×#108 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861215 | 2 |
| C2×#16861145 | 2 |
| #22549858 | 2 |
| C127⋊#338 | 2 |
| C2×#108×C127 | 2 |
| #1813 | 127 |