Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #22550678 | C2 | semidirect |
| 2. #22550311 | C2 | semidirect |
| 3. C2×D2032 | C2 | semidirect |
| 4. #22550147 | C2 | semidirect |
| 5. #22549688 | C2 | semidirect |
| 6. #22549659 | C2 | semidirect |
| 7. #359×C127 | C2 | semidirect |
| 14. C2×D1016 | C22 | semidirect |
| 20. #16861149 | C22 | semidirect |
| 23. C2×C16×C127 | C22 | semidirect |
| 24. #108×C127 | C22 | semidirect |
| 94. C127 | #2192 | semidirect |
| 100. #359 | D127 | semidirect |
| 116. C2×C16 | C2×D127 | semidirect |
| 117. #108 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550678 | 2 |
| #22550311 | 2 |
| C2×D2032 | 2 |
| #22550147 | 2 |
| #22549688 | 2 |
| #22549659 | 2 |
| #359×C127 | 2 |
| #2192 | 127 |