Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic254 | C2 | semidirect |
| 3. #22550223 | C2 | semidirect |
| 4. #22550221 | C2 | semidirect |
| 5. #22550166 | C2 | semidirect |
| 6. #22550165 | C2 | semidirect |
| 7. #22550076 | C2 | semidirect |
| 8. #22550074 | C2 | semidirect |
| 9. C8×Dic254 | C2 | semidirect |
| 10. #22549961 | C2 | semidirect |
| 11. C4×SD16×C127 | C2 | semidirect |
| 77. Dic254 | SD16 | semidirect |
| 91. Q8×C127 | #41 | semidirect |
| 126. C127 | #3362 | semidirect |
| 137. C4×SD16 | D127 | semidirect |
| 206. Q8 | #14523248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic254 | 2 |
| #22550547 | 2 |
| #22550223 | 2 |
| #22550221 | 2 |
| #22550166 | 2 |
| #22550165 | 2 |
| #22550076 | 2 |
| #22550074 | 2 |
| C8×Dic254 | 2 |
| #22549961 | 2 |
| C4×SD16×C127 | 2 |
| #3362 | 127 |