Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22549982 | C2 | semidirect |
| 4. #22549691 | C2 | semidirect |
| 6. #22549653 | C2 | semidirect |
| 7. #365×C127 | C2 | semidirect |
| 12. Dic1016 | C4 | semidirect |
| 13. #16861154 | C4 | semidirect |
| 65. C127 | #2180 | semidirect |
| 69. #365 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550319 | 2 |
| #22549997 | 2 |
| #22549982 | 2 |
| #22549691 | 2 |
| #22549685 | 2 |
| #22549653 | 2 |
| #365×C127 | 2 |
| #2180 | 127 |