Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D127 | C2 | semidirect |
| 3. #22550172 | C2 | semidirect |
| 4. #22550168 | C2 | semidirect |
| 5. #22550166 | C2 | semidirect |
| 6. #22550160 | C2 | semidirect |
| 7. #22550154 | C2 | semidirect |
| 8. #22549915 | C2 | semidirect |
| 9. #22549898 | C2 | semidirect |
| 11. #476×C127 | C2 | semidirect |
| 44. #14523247 | Q8 | semidirect |
| 86. Dic254 | C2×Q8 | semidirect |
| 105. D4×C127 | C2×Q8 | semidirect |
| 138. C127 | #3079 | semidirect |
| 144. #476 | D127 | semidirect |
| 229. D4 | Q8×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D127 | 2 |
| C4×#14523247 | 2 |
| #22550172 | 2 |
| #22550168 | 2 |
| #22550166 | 2 |
| #22550160 | 2 |
| #22550154 | 2 |
| #22549915 | 2 |
| #22549898 | 2 |
| #22549874 | 2 |
| #476×C127 | 2 |
| #3079 | 127 |