Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#16861231 | C2 | semidirect |
| 2. C2×#16861229 | C2 | semidirect |
| 3. #22550422 | C2 | semidirect |
| 4. #22550261 | C2 | semidirect |
| 5. #22550259 | C2 | semidirect |
| 6. #22550257 | C2 | semidirect |
| 7. #22550254 | C2 | semidirect |
| 8. #22550251 | C2 | semidirect |
| 9. #22550247 | C2 | semidirect |
| 10. C2×C8×Dic127 | C2 | semidirect |
| 11. C2×#135×C127 | C2 | semidirect |
| 55. C2×C127⋊C8 | D4 | semidirect |
| 74. C2×C8×C127 | D4 | semidirect |
| 119. Dic127 | #135 | semidirect |
| 126. C127 | #3147 | semidirect |
| 129. C2×#135 | D127 | semidirect |
| 194. C2×C8 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| C2×#16861229 | 2 |
| #22550422 | 2 |
| #22550261 | 2 |
| #22550259 | 2 |
| #22550257 | 2 |
| #22550254 | 2 |
| #22550251 | 2 |
| #22550247 | 2 |
| C2×C8×Dic127 | 2 |
| C2×#135×C127 | 2 |
| #3147 | 127 |