Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
256 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22549623 | C2 | semidirect |
| 5. #22549622 | C2 | semidirect |
| 6. #22549621 | C2 | semidirect |
| 7. #332×C127 | C2 | semidirect |
| 91. D127 | #332 | direct (N × H) |
| 93. C127 | C2×#332 | semidirect |
| 100. #332 | D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D127 | 2 |
| C4⋊C8×D127 | 2 |
| #22549623 | 2 |
| #22549622 | 2 |
| #22549621 | 2 |
| #332×C127 | 2 |
| C2×#332 | 127 |