Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 1. C2×#16861217 | C2 | semidirect |
| 3. #22549953 | C2 | semidirect |
| 4. #22549941 | C2 | semidirect |
| 5. #22549844 | C2 | semidirect |
| 6. C2×C4×C127⋊C8 | C2 | semidirect |
| 7. #423×C127 | C2 | semidirect |
| 34. C2×C127⋊C8 | D4 | semidirect |
| 75. C4×C127 | #131 | semidirect |
| 84. C127 | #2931 | semidirect |
| 89. #423 | D127 | semidirect |
| 160. C4 | #16861217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861217 | 2 |
| #22550426 | 2 |
| #22549953 | 2 |
| #22549941 | 2 |
| #22549844 | 2 |
| C2×C4×C127⋊C8 | 2 |
| #423×C127 | 2 |
| #2931 | 127 |