Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×#14523231 | C2 | semidirect |
| 3. C2×#16861167 | C2 | semidirect |
| 4. #22549879 | C2 | direct (N × H) |
| 5. C2×#16861131 | C2 | semidirect |
| 6. C2×#16861130 | C2 | semidirect |
| 7. C2×#16861129 | C2 | semidirect |
| 8. C2×#102×C127 | C2 | semidirect |
| 14. C2×D4×D127 | C4 | semidirect |
| 18. C2×#14523231 | C22 | semidirect |
| 19. C22×C127⋊C8 | C22 | semidirect |
| 21. #16861167 | C22 | semidirect |
| 22. C2×C4⋊Dic127 | C22 | semidirect |
| 25. #16861131 | C22 | semidirect |
| 26. #16861130 | C22 | semidirect |
| 27. #16861129 | C22 | semidirect |
| 29. C22×C8×C127 | C22 | semidirect |
| 30. C2×C4⋊C4×C127 | C22 | semidirect |
| 31. #102×C127 | C22 | semidirect |
| 46. D4×D127 | C2×C4 | semidirect |
| 55. C2×C127⋊C8 | C23 | semidirect |
| 57. C4⋊Dic127 | C23 | semidirect |
| 68. C2×C8×C127 | C23 | semidirect |
| 70. C4⋊C4×C127 | C23 | semidirect |
| 134. C2×C127 | #418 | semidirect |
| 141. C127 | C2×#418 | semidirect |
| 149. C2×#102 | D127 | semidirect |
| 162. C22×C8 | C2×D127 | semidirect |
| 166. C2×C4⋊C4 | C2×D127 | semidirect |
| 172. #102 | C2×D127 | semidirect |
| 205. C2×C8 | C22×D127 | semidirect |
| 209. C4⋊C4 | C22×D127 | semidirect |
| 277. C2 | #22549879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D127 | 2 |
| C22×#14523231 | 2 |
| C2×#16861167 | 2 |
| #22549879 | 2 |
| C2×#16861131 | 2 |
| C2×#16861130 | 2 |
| C2×#16861129 | 2 |
| C2×#102×C127 | 2 |
| C2×#418 | 127 |