Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22549984 | C2 | semidirect |
| 4. #22549699 | C2 | semidirect |
| 5. #22549693 | C2 | semidirect |
| 7. #347×C127 | C2 | semidirect |
| 12. Dic1016 | C4 | semidirect |
| 13. #16861154 | C4 | semidirect |
| 65. C127 | #2180 | semidirect |
| 72. #347 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550319 | 2 |
| #22549999 | 2 |
| #22549984 | 2 |
| #22549699 | 2 |
| #22549693 | 2 |
| #22549687 | 2 |
| #347×C127 | 2 |
| #2180 | 127 |