Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 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 |
|---|---|---|
| 1. #22550605 | C2 | semidirect |
| 5. #22549623 | C2 | semidirect |
| 6. #22549608 | C2 | semidirect |
| 7. Q8⋊C8×C127 | C2 | semidirect |
| 64. Q8×C127 | SD16 | semidirect |
| 91. C127 | #1626 | semidirect |
| 98. Q8⋊C8 | D127 | semidirect |
| 146. Q8 | #14523237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550605 | 2 |
| #22550223 | 2 |
| #22550077 | 2 |
| #22550076 | 2 |
| #22549623 | 2 |
| #22549608 | 2 |
| Q8⋊C8×C127 | 2 |
| #1626 | 127 |