Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×#16861240 | C2 | semidirect |
| 3. #22550098 | C2 | semidirect |
| 4. #22550086 | C2 | semidirect |
| 5. #22550076 | C2 | semidirect |
| 6. #22549900 | C2 | semidirect |
| 7. #22549875 | C2 | semidirect |
| 8. C2×C4×Q8×C127 | C2 | semidirect |
| 52. C2×Q8×C127 | D4 | semidirect |
| 111. C4×C127 | #137 | semidirect |
| 121. C127 | #3037 | semidirect |
| 124. C2×C4×Q8 | D127 | semidirect |
| 160. C2×Q8 | D508 | semidirect |
| 233. C4 | #16861240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861240 | 2 |
| #22550426 | 2 |
| #22550098 | 2 |
| #22550086 | 2 |
| #22550076 | 2 |
| #22549900 | 2 |
| #22549875 | 2 |
| C2×C4×Q8×C127 | 2 |
| #3037 | 127 |