Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
716 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 249 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. #22550354 | C2 | semidirect |
| 3. #22549849 | C2 | semidirect |
| 4. #519×C127 | C2 | semidirect |
| 7. C2×#14523249 | C4 | semidirect |
| 9. C2×Q8×D127 | C4 | semidirect |
| 64. C127 | #2884 | semidirect |
| 67. #519 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861257 | 2 |
| #22550354 | 2 |
| #22549849 | 2 |
| #519×C127 | 2 |
| #2884 | 127 |