Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#16861155 | C2 | semidirect |
| 3. #22549679 | C2 | semidirect |
| 53. C22×C127 | Q32 | semidirect |
| 66. C127 | #2188 | semidirect |
| 119. C22 | #16861155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic508 | 2 |
| C2×#16861155 | 2 |
| #22549679 | 2 |
| C22⋊(C127⋊C16) | 2 |
| #467×C127 | 2 |
| #2188 | 127 |