Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #22550358 | C2 | semidirect |
| 3. #22549989 | C2 | semidirect |
| 4. #22549987 | C2 | semidirect |
| 5. #22549983 | C2 | semidirect |
| 6. C4×#14523235 | C2 | semidirect |
| 7. #22549961 | C2 | semidirect |
| 8. #106×D127 | C2 | semidirect |
| 9. #22549876 | C2 | semidirect |
| 10. #22549833 | C2 | semidirect |
| 11. #441×C127 | C2 | semidirect |
| 13. #16861232 | C4 | semidirect |
| 41. #14523249 | C2×C4 | semidirect |
| 49. #14523235 | C2×C4 | semidirect |
| 50. D1016 | C2×C4 | semidirect |
| 54. C8×D127 | C2×C4 | semidirect |
| 65. Q16×C127 | C2×C4 | semidirect |
| 115. C127 | #2952 | semidirect |
| 121. #441 | D127 | semidirect |
| 165. Q16 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| #22550358 | 2 |
| #22549989 | 2 |
| #22549987 | 2 |
| #22549983 | 2 |
| C4×#14523235 | 2 |
| #22549961 | 2 |
| #106×D127 | 2 |
| #22549876 | 2 |
| #22549833 | 2 |
| #441×C127 | 2 |
| #2952 | 127 |