Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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 |
|---|---|---|
| 1. C22×#14523247 | C2 | semidirect |
| 2. #22550424 | C2 | direct (N × H) |
| 3. C2×#16861209 | C2 | semidirect |
| 4. C2×#16861196 | C2 | semidirect |
| 5. C2×#16861180 | C2 | semidirect |
| 6. C2×D4×Dic127 | C2 | semidirect |
| 7. C2×C42×D127 | C2 | semidirect |
| 8. C2×#127×C127 | C2 | semidirect |
| 10. C2×#14523247 | C22 | semidirect |
| 16. #16861209 | C22 | semidirect |
| 17. #16861196 | C22 | semidirect |
| 18. #16861180 | C22 | semidirect |
| 19. D4×Dic127 | C22 | semidirect |
| 24. C42×D127 | C22 | semidirect |
| 27. #127×C127 | C22 | semidirect |
| 41. C2×C4×D127 | D4 | semidirect |
| 69. C4×D127 | C2×D4 | semidirect |
| 77. C2×C4×C127 | #41 | semidirect |
| 90. C4×C127 | C2×#41 | semidirect |
| 95. C2×C127 | #532 | semidirect |
| 100. C127 | C2×#532 | semidirect |
| 104. C2×#127 | D127 | semidirect |
| 119. #127 | C2×D127 | semidirect |
| 177. C2×C4 | #14523247 | semidirect |
| 193. C4 | C2×#14523247 | semidirect |
| 196. C2 | #22550424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523247 | 2 |
| #22550424 | 2 |
| C2×#16861209 | 2 |
| C2×#16861196 | 2 |
| C2×#16861180 | 2 |
| C2×D4×Dic127 | 2 |
| C2×C42×D127 | 2 |
| C2×#127×C127 | 2 |
| C2×#532 | 127 |