Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×Dic127⋊C8 | C2 | semidirect |
| 3. C2×#16861134 | C2 | semidirect |
| 4. C2×#16861132 | C2 | semidirect |
| 6. C4⋊C4×Dic127 | C2 | semidirect |
| 11. #16861196 | C4 | semidirect |
| 131. C127 | #1983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861196 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861134 | 2 |
| C2×#16861132 | 2 |
| C2×#16861130 | 2 |
| C4⋊C4×Dic127 | 2 |
| C2×#102×C127 | 2 |
| #1983 | 127 |