Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14523237 | C2 | semidirect |
| 2. C22×C8×D127 | C2 | semidirect |
| 3. C2×#16861189 | C2 | semidirect |
| 5. #22550106 | C2 | direct (N × H) |
| 6. C2×#16861132 | C2 | semidirect |
| 7. C2×#16861129 | C2 | semidirect |
| 8. C2×#106×C127 | C2 | semidirect |
| 14. C2×#14523237 | C22 | semidirect |
| 17. C2×C8×D127 | C22 | semidirect |
| 19. #16861189 | C22 | semidirect |
| 25. #16861132 | C22 | semidirect |
| 26. #16861129 | C22 | semidirect |
| 30. #106×C127 | C22 | semidirect |
| 59. C2×C8×C127 | D4 | semidirect |
| 71. C22×D127 | SD16 | semidirect |
| 97. C8×C127 | C2×D4 | semidirect |
| 109. C2×D127 | C2×SD16 | semidirect |
| 117. C2×C127 | #465 | semidirect |
| 124. C127 | C2×#465 | semidirect |
| 130. C2×#106 | D127 | semidirect |
| 152. #106 | C2×D127 | semidirect |
| 180. C2×C8 | D508 | semidirect |
| 221. C8 | C2×D508 | semidirect |
| 243. C2 | #22550106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523237 | 2 |
| C22×C8×D127 | 2 |
| C2×#16861189 | 2 |
| C2×#16861184 | 2 |
| #22550106 | 2 |
| C2×#16861132 | 2 |
| C2×#16861129 | 2 |
| C2×#106×C127 | 2 |
| C2×#465 | 127 |