Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C2×#16861207 | C2 | semidirect |
| 5. #22550080 | C2 | direct (N × H) |
| 6. C2×Dic127⋊C8 | C2 | semidirect |
| 7. C2×#16861132 | C2 | semidirect |
| 8. C2×#103×C127 | C2 | semidirect |
| 18. #16861207 | C22 | semidirect |
| 25. Dic127⋊C8 | C22 | semidirect |
| 26. #16861132 | C22 | semidirect |
| 30. #103×C127 | C22 | semidirect |
| 78. C2×Dic127 | SD16 | semidirect |
| 111. Dic127 | C2×SD16 | semidirect |
| 112. C2×C127 | #461 | semidirect |
| 118. C127 | C2×#461 | semidirect |
| 126. C2×#103 | D127 | semidirect |
| 148. #103 | C2×D127 | semidirect |
| 231. C2 | #22550080 | 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×#14523235 | 2 |
| C2×#16861207 | 2 |
| C2×#16861171 | 2 |
| #22550080 | 2 |
| C2×Dic127⋊C8 | 2 |
| C2×#16861132 | 2 |
| C2×#103×C127 | 2 |
| C2×#461 | 127 |