Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16861136 | C2 | semidirect |
| 2. C4×#14523232 | C2 | semidirect |
| 3. C4×C4⋊Dic127 | C2 | semidirect |
| 13. C4⋊Q8×C127 | C4 | semidirect |
| 14. #127×C127 | C4 | semidirect |
| 15. #124×C127 | C4 | semidirect |
| 23. #14523232 | D4 | semidirect |
| 82. C4×C127 | #104 | semidirect |
| 93. C127 | #1980 | semidirect |
| 100. C4⋊Q8 | Dic127 | semidirect |
| 101. #127 | Dic127 | semidirect |
| 102. #124 | Dic127 | semidirect |
| 176. C4 | #16861136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861136 | 2 |
| C4×#14523232 | 2 |
| C4×C4⋊Dic127 | 2 |
| #532×C127 | 2 |
| #1980 | 127 |