Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22549645 | C2 | semidirect |
| 5. #343×C127 | C2 | semidirect |
| 13. #16861125 | C4 | semidirect |
| 29. #14523232 | C2×C4 | semidirect |
| 37. M16×C127 | C2×C4 | semidirect |
| 78. Dic127 | #100 | semidirect |
| 86. C127 | C4×#100 | semidirect |
| 91. #343 | D127 | semidirect |
| 119. M16 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861171 | 2 |
| C2×#16861125 | 2 |
| M16×Dic127 | 2 |
| #22549645 | 2 |
| #343×C127 | 2 |
| C4×#100 | 127 |