Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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. #22549783 | C2 | semidirect |
| 5. #22549782 | C2 | semidirect |
| 6. #22549781 | C2 | semidirect |
| 7. #22549780 | C2 | semidirect |
| 9. #391×C127 | C2 | semidirect |
| 14. C2×Q8×D127 | C4 | semidirect |
| 123. C127 | #2310 | semidirect |
| 131. #391 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D127 | 2 |
| C2×#16861167 | 2 |
| C2×#16861166 | 2 |
| #22549783 | 2 |
| #22549782 | 2 |
| #22549781 | 2 |
| #22549780 | 2 |
| #22549738 | 2 |
| #391×C127 | 2 |
| #2310 | 127 |