Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #22550284 | C2 | semidirect |
| 3. #22550282 | C2 | semidirect |
| 4. #22550280 | C2 | semidirect |
| 5. #22550278 | C2 | semidirect |
| 6. #22550277 | C2 | semidirect |
| 11. #500×C127 | C2 | semidirect |
| 42. #14523231 | Q8 | semidirect |
| 45. C8×D127 | Q8 | semidirect |
| 108. C127 | #3164 | semidirect |
| 113. #500 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550503 | 2 |
| #22550284 | 2 |
| #22550282 | 2 |
| #22550280 | 2 |
| #22550278 | 2 |
| #22550277 | 2 |
| #22549917 | 2 |
| #22549913 | 2 |
| #107×D127 | 2 |
| #22549830 | 2 |
| #500×C127 | 2 |
| #3164 | 127 |