Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22550279 | C2 | semidirect |
| 3. #22550209 | C2 | semidirect |
| 4. #22550200 | C2 | semidirect |
| 5. #22550161 | C2 | semidirect |
| 6. #22550153 | C2 | semidirect |
| 7. #22550124 | C2 | semidirect |
| 8. C4×#14523235 | C2 | semidirect |
| 9. #22549954 | C2 | semidirect |
| 10. #22549919 | C2 | semidirect |
| 11. #556×C127 | C2 | semidirect |
| 85. C127⋊C8 | #41 | semidirect |
| 123. C127 | #3353 | semidirect |
| 124. #556 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550530 | 2 |
| #22550279 | 2 |
| #22550209 | 2 |
| #22550200 | 2 |
| #22550161 | 2 |
| #22550153 | 2 |
| #22550124 | 2 |
| C4×#14523235 | 2 |
| #22549954 | 2 |
| #22549919 | 2 |
| #556×C127 | 2 |
| #3353 | 127 |