Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #22550286 | C2 | semidirect |
| 4. #22550285 | C2 | semidirect |
| 5. #22550282 | C2 | semidirect |
| 6. #22550280 | C2 | semidirect |
| 7. #22550273 | C2 | semidirect |
| 11. #501×C127 | C2 | semidirect |
| 52. #14523231 | Q8 | semidirect |
| 95. C127⋊C8 | C2×Q8 | semidirect |
| 103. C8×C127 | C2×Q8 | semidirect |
| 125. C127 | #3165 | semidirect |
| 131. #501 | D127 | semidirect |
| 228. C8 | Q8×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550432 | 2 |
| C4⋊Q8×D127 | 2 |
| #22550286 | 2 |
| #22550285 | 2 |
| #22550282 | 2 |
| #22550280 | 2 |
| #22550273 | 2 |
| #22549917 | 2 |
| #22549915 | 2 |
| #22549828 | 2 |
| #501×C127 | 2 |
| #3165 | 127 |