Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
540 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
|---|---|---|
| 1. #22549783 | C2 | semidirect |
| 2. #22549769 | C2 | semidirect |
| 3. #22549769 | C2 | semidirect |
| 5. #22549751 | C2 | semidirect |
| 6. #22549744 | C2 | semidirect |
| 7. C4×C4⋊Dic127 | C2 | semidirect |
| 8. C22⋊C4×Dic127 | C2 | semidirect |
| 28. #124×C127 | C4 | semidirect |
| 49. C2×Q8×C127 | C2×C4 | semidirect |
| 56. C22⋊C4×C127 | C2×C4 | semidirect |
| 57. C22⋊C4×C127 | C2×C4 | semidirect |
| 58. C42×C127 | C2×C4 | semidirect |
| 119. C127 | #2337 | semidirect |
| 132. #124 | Dic127 | semidirect |
| 153. C2×Q8 | C2×Dic127 | semidirect |
| 172. C22⋊C4 | C2×Dic127 | semidirect |
| 173. C22⋊C4 | C2×Dic127 | semidirect |
| 177. C42 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549783 | 2 |
| #22549769 | 2 |
| #22549756 | 2 |
| #22549751 | 2 |
| #22549744 | 2 |
| C4×C4⋊Dic127 | 2 |
| C22⋊C4×Dic127 | 2 |
| C2×#124×C127 | 2 |
| #2337 | 127 |