Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
656 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 261 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. #22549746 | C2 | semidirect |
| 4. #22549741 | C2 | semidirect |
| 6. C4⋊C4×Dic127 | C2 | semidirect |
| 7. #384×C127 | C2 | semidirect |
| 17. C42×D127 | C4 | semidirect |
| 58. C4×D127 | C4⋊C4 | semidirect |
| 80. C4×C127 | #117 | semidirect |
| 91. C127 | #2285 | semidirect |
| 95. #384 | D127 | semidirect |
| 174. C4 | #16861167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861167 | 2 |
| C2×C42×D127 | 2 |
| #22549746 | 2 |
| #22549741 | 2 |
| #22549733 | 2 |
| C4⋊C4×Dic127 | 2 |
| #384×C127 | 2 |
| #2285 | 127 |