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. #22549983 | C2 | semidirect |
| 4. #22549700 | C2 | semidirect |
| 6. #22549653 | C2 | semidirect |
| 7. #362×C127 | C2 | semidirect |
| 11. #16861155 | C4 | semidirect |
| 12. #16861152 | C4 | semidirect |
| 65. C127 | #2180 | semidirect |
| 70. #362 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550317 | 2 |
| #22549997 | 2 |
| #22549983 | 2 |
| #22549700 | 2 |
| #22549687 | 2 |
| #22549653 | 2 |
| #362×C127 | 2 |
| #2180 | 127 |