Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22550161 | C2 | semidirect |
| 4. #22549627 | C2 | semidirect |
| 5. #22549623 | C2 | semidirect |
| 7. C8×Q8×C127 | C2 | semidirect |
| 54. Q8×C127 | SD16 | semidirect |
| 62. C8×C127 | SD16 | semidirect |
| 80. C127 | #1666 | semidirect |
| 84. C8×Q8 | D127 | semidirect |
| 126. Q8 | #14523237 | semidirect |
| 142. C8 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550249 | 2 |
| #22550161 | 2 |
| #22550076 | 2 |
| #22549627 | 2 |
| #22549623 | 2 |
| #22549619 | 2 |
| C8×Q8×C127 | 2 |
| #1666 | 127 |