Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22549628 | C2 | semidirect |
| 4. Q8⋊(C127⋊C8) | C2 | semidirect |
| 6. #22549598 | C2 | semidirect |
| 7. #446×C127 | C2 | semidirect |
| 78. C127 | #1585 | semidirect |
| 79. #446 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523235 | 2 |
| C8×D508 | 2 |
| #22549628 | 2 |
| Q8⋊(C127⋊C8) | 2 |
| #22549603 | 2 |
| #22549598 | 2 |
| #446×C127 | 2 |
| #1585 | 127 |