Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #22549917 | C2 | semidirect |
| 4. #22549915 | C2 | semidirect |
| 5. #22549914 | C2 | semidirect |
| 6. #22549912 | C2 | semidirect |
| 7. #427×C127 | C2 | semidirect |
| 9. C2×#14523231 | C4 | semidirect |
| 20. #16861143 | C22 | semidirect |
| 21. #16861142 | C22 | semidirect |
| 22. #16861141 | C22 | semidirect |
| 23. #16861140 | C22 | semidirect |
| 26. #107×C127 | C22 | semidirect |
| 27. #106×C127 | C22 | semidirect |
| 35. #14523231 | C2×C4 | semidirect |
| 36. #14523231 | C2×C4 | semidirect |
| 37. C2×C127⋊C8 | C2×C4 | semidirect |
| 46. C2×C8×C127 | C2×C4 | semidirect |
| 88. C127 | #2911 | semidirect |
| 95. #427 | D127 | semidirect |
| 112. #107 | C2×D127 | semidirect |
| 115. #106 | C2×D127 | semidirect |
| 128. C2×C8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523231 | 2 |
| #117×D127 | 2 |
| #22549917 | 2 |
| #22549915 | 2 |
| #22549914 | 2 |
| #22549912 | 2 |
| #427×C127 | 2 |
| #2911 | 127 |