Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16861200 | C2 | semidirect |
| 3. #22550186 | C2 | semidirect |
| 4. #22550182 | C2 | semidirect |
| 5. #22550179 | C2 | semidirect |
| 6. #22550175 | C2 | semidirect |
| 7. #22549919 | C2 | semidirect |
| 8. #22549899 | C2 | semidirect |
| 11. #428×C127 | C2 | semidirect |
| 136. C127 | #3080 | semidirect |
| 144. #428 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861200 | 2 |
| #22550344 | 2 |
| #22550186 | 2 |
| #22550182 | 2 |
| #22550179 | 2 |
| #22550175 | 2 |
| #22549919 | 2 |
| #22549899 | 2 |
| #22549878 | 2 |
| #22549875 | 2 |
| #428×C127 | 2 |
| #3080 | 127 |