Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
| 92. C127 | #1546 | semidirect |
| 99. #332 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D127 | 2 |
| #22549928 | 2 |
| #22549898 | 2 |
| #22549623 | 2 |
| #22549622 | 2 |
| #22549621 | 2 |
| #332×C127 | 2 |
| #1546 | 127 |