Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×Q8×Dic127 | C2 | semidirect |
| 5. #22549768 | C2 | semidirect |
| 6. #22549741 | C2 | semidirect |
| 7. #22549723 | C2 | semidirect |
| 8. C42×Dic127 | C2 | semidirect |
| 9. #391×C127 | C2 | semidirect |
| 12. #16861198 | C4 | semidirect |
| 44. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 48. C4×Dic127 | C2×C4 | semidirect |
| 52. C2×Q8×C127 | C2×C4 | semidirect |
| 105. Dic127 | #124 | semidirect |
| 113. C127 | C4×#124 | semidirect |
| 117. #391 | D127 | semidirect |
| 146. C2×Q8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861198 | 2 |
| C2×Q8×Dic127 | 2 |
| C2×#16861171 | 2 |
| #22549778 | 2 |
| #22549768 | 2 |
| #22549741 | 2 |
| #22549723 | 2 |
| C42×Dic127 | 2 |
| #391×C127 | 2 |
| C4×#124 | 127 |