Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #22550083 | C2 | semidirect |
| 4. #22550078 | C2 | semidirect |
| 5. #22549900 | C2 | semidirect |
| 6. #22549885 | C2 | semidirect |
| 7. C2×C4⋊Q8×C127 | C2 | semidirect |
| 88. C4×C127 | #137 | semidirect |
| 98. C127 | #3039 | semidirect |
| 100. C2×C4⋊Q8 | D127 | semidirect |
| 188. C4 | #16861240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861240 | 2 |
| C4×#14523248 | 2 |
| #22550083 | 2 |
| #22550078 | 2 |
| #22549900 | 2 |
| #22549885 | 2 |
| C2×C4⋊Q8×C127 | 2 |
| #3039 | 127 |