Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22550238 | C2 | direct (N × H) |
| 3. C2×#16861132 | C2 | semidirect |
| 5. C2×#16861120 | C2 | semidirect |
| 6. C2×C4⋊Q8×C127 | C2 | semidirect |
| 14. #16861132 | C22 | semidirect |
| 16. #16861120 | C22 | semidirect |
| 19. C4⋊Q8×C127 | C22 | semidirect |
| 82. C2×C127 | #489 | semidirect |
| 88. C127 | C2×#489 | semidirect |
| 89. C2×C4⋊Q8 | D127 | semidirect |
| 100. C4⋊Q8 | C2×D127 | semidirect |
| 171. C2 | #22550238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861197 | 2 |
| #22550238 | 2 |
| C2×#16861132 | 2 |
| C2×#16861129 | 2 |
| C2×#16861120 | 2 |
| C2×C4⋊Q8×C127 | 2 |
| C2×#489 | 127 |