Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16861208 | C2 | semidirect |
| 3. #22550170 | C2 | semidirect |
| 4. #22550165 | C2 | semidirect |
| 5. #22550160 | C2 | semidirect |
| 6. #22550155 | C2 | semidirect |
| 7. #22549919 | C2 | semidirect |
| 8. #22549899 | C2 | semidirect |
| 11. #428×C127 | C2 | semidirect |
| 44. #14523248 | Q8 | semidirect |
| 87. Dic254 | C2×Q8 | semidirect |
| 89. D508 | C2×Q8 | semidirect |
| 139. C127 | #3079 | semidirect |
| 147. #428 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861208 | 2 |
| #22550344 | 2 |
| #22550170 | 2 |
| #22550165 | 2 |
| #22550160 | 2 |
| #22550155 | 2 |
| #22549919 | 2 |
| #22549899 | 2 |
| #22549878 | 2 |
| #22549875 | 2 |
| #428×C127 | 2 |
| #3079 | 127 |