Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#16861216 | C2 | semidirect |
| 2. #22549998 | C2 | semidirect |
| 3. #22549993 | C2 | semidirect |
| 4. #22549925 | C2 | semidirect |
| 5. #22549893 | C2 | semidirect |
| 6. #22549834 | C2 | semidirect |
| 10. #16861216 | C22 | semidirect |
| 11. #16861216 | C22 | semidirect |
| 17. #16861145 | C22 | semidirect |
| 18. #16861136 | C22 | semidirect |
| 19. #16861119 | C22 | semidirect |
| 20. C8×Dic127 | C22 | semidirect |
| 22. #137×C127 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C127 | C4 | semidirect |
| 90. C127 | #2955 | semidirect |
| 99. #137 | Dic127 | semidirect |
| 100. AGL(1,ℤ/8) | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861216 | 2 |
| #22549998 | 2 |
| #22549993 | 2 |
| #22549925 | 2 |
| #22549893 | 2 |
| #22549834 | 2 |
| #575×C127 | 2 |
| #2955 | 127 |