Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
696 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 389 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. C4⋊C4×Dic127 | C2 | semidirect |
| 5. #16861168 | C4 | semidirect |
| 13. C2×C4⋊C4×C127 | C4 | semidirect |
| 16. C4⋊Dic127 | C2×C4 | semidirect |
| 19. C4×Dic127 | C2×C4 | semidirect |
| 38. C2×C4×C127 | C42 | semidirect |
| 60. C127 | #2274 | semidirect |
| 69. C2×C4⋊C4 | Dic127 | semidirect |
| 98. C2×C4 | C4×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861168 | 2 |
| C4⋊C4×Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| C22×C4⋊C4×C127 | 2 |
| #2274 | 127 |