Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
524 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22549758 | C2 | semidirect |
| 4. C4×Dic127⋊C4 | C2 | semidirect |
| 6. C42×Dic127 | C2 | semidirect |
| 7. #376×C127 | C2 | semidirect |
| 9. #16861166 | C4 | semidirect |
| 76. C127 | #2298 | semidirect |
| 82. #376 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861166 | 2 |
| #22549765 | 2 |
| #22549758 | 2 |
| C4×Dic127⋊C4 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| C42×Dic127 | 2 |
| #376×C127 | 2 |
| #2298 | 127 |