Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #22549886 | C2 | semidirect |
| 5. #22549781 | C2 | semidirect |
| 6. #22549637 | C2 | semidirect |
| 7. #343×C127 | C2 | semidirect |
| 11. #16861242 | C4 | semidirect |
| 37. C2×Dic254 | C2×C4 | semidirect |
| 61. M16×C127 | C2×C4 | semidirect |
| 125. C127 | #1882 | semidirect |
| 131. #343 | D127 | semidirect |
| 177. M16 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861242 | 2 |
| #22550357 | 2 |
| C2×#16861135 | 2 |
| #22549886 | 2 |
| #22549781 | 2 |
| #22549637 | 2 |
| #343×C127 | 2 |
| #1882 | 127 |