Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22550353 | C2 | semidirect |
| 4. #22549973 | C2 | semidirect |
| 5. #22549967 | C2 | semidirect |
| 6. #22549912 | C2 | semidirect |
| 7. #22549886 | C2 | semidirect |
| 8. #22549834 | C2 | semidirect |
| 11. C2×#14523236 | C4 | semidirect |
| 16. #16861174 | C22 | semidirect |
| 23. #16861142 | C22 | semidirect |
| 24. #16861140 | C22 | semidirect |
| 25. #16861134 | C22 | semidirect |
| 26. #16861119 | C22 | semidirect |
| 27. C8×Dic127 | C22 | semidirect |
| 34. C2×Dic254 | C2×C4 | semidirect |
| 38. #14523236 | C2×C4 | semidirect |
| 39. #14523236 | C2×C4 | semidirect |
| 40. C2×C127⋊C8 | C2×C4 | semidirect |
| 104. C127 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523236 | 2 |
| #22550353 | 2 |
| #22550351 | 2 |
| #22549973 | 2 |
| #22549967 | 2 |
| #22549912 | 2 |
| #22549886 | 2 |
| #22549834 | 2 |
| #418×C127 | 2 |
| #2949 | 127 |