Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
560 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 2. #22549769 | C2 | semidirect |
| 3. #22549742 | C2 | semidirect |
| 4. #22549739 | C2 | semidirect |
| 5. C4⋊C4×Dic127 | C2 | semidirect |
| 6. C4×C4⋊Dic127 | C2 | semidirect |
| 7. C4×C22⋊Dic127 | C2 | semidirect |
| 22. C4×D4×C127 | C4 | semidirect |
| 98. C127 | #2357 | semidirect |
| 109. C4×D4 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549779 | 2 |
| #22549769 | 2 |
| #22549742 | 2 |
| #22549739 | 2 |
| C4⋊C4×Dic127 | 2 |
| C4×C4⋊Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| C2×C4×D4×C127 | 2 |
| #2357 | 127 |