Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 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. C4×#14523247 | C2 | semidirect |
| 3. #22549988 | C2 | semidirect |
| 4. #22549984 | C2 | semidirect |
| 5. #22549982 | C2 | semidirect |
| 6. #22549976 | C2 | semidirect |
| 7. #22549973 | C2 | semidirect |
| 8. #22549911 | C2 | semidirect |
| 9. #22549869 | C2 | semidirect |
| 10. #97×D127 | C2 | semidirect |
| 11. #442×C127 | C2 | semidirect |
| 13. #16861228 | C4 | semidirect |
| 41. #14523247 | C2×C4 | semidirect |
| 48. Dic508 | C2×C4 | semidirect |
| 49. #14523236 | C2×C4 | semidirect |
| 53. C8×D127 | C2×C4 | semidirect |
| 66. D8×C127 | C2×C4 | semidirect |
| 115. C127 | #2943 | semidirect |
| 119. #442 | D127 | semidirect |
| 167. D8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861228 | 2 |
| C4×#14523247 | 2 |
| #22549988 | 2 |
| #22549984 | 2 |
| #22549982 | 2 |
| #22549976 | 2 |
| #22549973 | 2 |
| #22549911 | 2 |
| #22549869 | 2 |
| #97×D127 | 2 |
| #442×C127 | 2 |
| #2943 | 127 |