Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
560 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
| 4. C22⋊C4×Dic127 | C2 | semidirect |
| 5. #22549722 | C2 | semidirect |
| 19. #124×C127 | C4 | semidirect |
| 34. C2×Q8×C127 | C2×C4 | semidirect |
| 41. C22⋊C4×C127 | C2×C4 | semidirect |
| 42. C42×C127 | C2×C4 | semidirect |
| 86. C127 | #2372 | semidirect |
| 96. #124 | Dic127 | semidirect |
| 111. C2×Q8 | C2×Dic127 | semidirect |
| 125. C22⋊C4 | C2×Dic127 | semidirect |
| 128. 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 |
| C22⋊C4×Dic127 | 2 |
| #22549722 | 2 |
| C2×#124×C127 | 2 |
| #2372 | 127 |