Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22550284 | C2 | semidirect |
| 6. #22550283 | C2 | semidirect |
| 7. #22550282 | C2 | semidirect |
| 11. #501×C127 | C2 | semidirect |
| 53. C8×D127 | Q8 | semidirect |
| 95. C127⋊C8 | C2×Q8 | semidirect |
| 103. C8×C127 | C2×Q8 | semidirect |
| 123. D127 | #501 | direct (N × H) |
| 125. C127 | C2×#501 | semidirect |
| 133. #501 | D127 | direct (N × H) |
| 228. C8 | 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 |
| #125×D127 | 2 |
| #22550286 | 2 |
| #22550285 | 2 |
| #22550284 | 2 |
| #22550283 | 2 |
| #22550282 | 2 |
| #107×D127 | 2 |
| #106×D127 | 2 |
| #97×D127 | 2 |
| #501×C127 | 2 |
| C2×#501 | 127 |