Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22549938 | C2 | semidirect |
| 3. #22549935 | C2 | semidirect |
| 4. #22549899 | C2 | semidirect |
| 6. C4×#14523232 | C2 | semidirect |
| 7. C4×M16×C127 | C2 | semidirect |
| 16. Dic127⋊C8 | C22 | semidirect |
| 18. #16861120 | C22 | semidirect |
| 19. C4×C127⋊C8 | C22 | semidirect |
| 22. #97×C127 | C22 | semidirect |
| 23. C4×C8×C127 | C22 | semidirect |
| 80. C127 | #2921 | semidirect |
| 87. C4×M16 | D127 | semidirect |
| 101. #97 | C2×D127 | semidirect |
| 103. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861166 | 2 |
| #22549938 | 2 |
| #22549935 | 2 |
| #22549899 | 2 |
| #22549839 | 2 |
| C4×#14523232 | 2 |
| C4×M16×C127 | 2 |
| #2921 | 127 |