Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
320 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4×#14523232 | C2 | semidirect |
| 3. #22549722 | C2 | semidirect |
| 4. #22549635 | C2 | semidirect |
| 8. #16861136 | C4 | semidirect |
| 13. C4×Q8×C127 | C4 | semidirect |
| 15. C4×D4×C127 | C4 | semidirect |
| 22. #14523232 | C2×C4 | semidirect |
| 25. C4×Dic127 | C2×C4 | semidirect |
| 83. C127 | #1759 | semidirect |
| 91. C4×Q8 | Dic127 | semidirect |
| 93. C4×D4 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861136 | 2 |
| C4×#14523232 | 2 |
| #22549722 | 2 |
| #22549635 | 2 |
| C4×#41×C127 | 2 |
| #1759 | 127 |