Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 119 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. M16×Dic127 | C2 | semidirect |
| 4. #22549644 | C2 | semidirect |
| 13. #16861126 | C4 | semidirect |
| 18. #100×C127 | C4 | semidirect |
| 26. #14523232 | C2×C4 | semidirect |
| 39. M16×C127 | C2×C4 | semidirect |
| 79. Dic127 | #100 | direct (N × H) |
| 87. C127 | C4×#100 | semidirect |
| 103. #100 | Dic127 | direct (N × H) |
| 121. M16 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic127 | 2 |
| C2×#16861126 | 2 |
| M16×Dic127 | 2 |
| #22549644 | 2 |
| C2×#100×C127 | 2 |
| C4×#100 | 127 |