Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. C22×C4⋊Dic127 | C2 | semidirect |
| 3. #22550195 | C2 | direct (N × H) |
| 4. C2×#16861141 | C2 | semidirect |
| 5. C2×#16861131 | C2 | semidirect |
| 6. C2×C22⋊C8×C127 | C2 | semidirect |
| 16. C2×C4⋊Dic127 | C22 | semidirect |
| 18. #16861141 | C22 | semidirect |
| 19. #16861131 | C22 | semidirect |
| 22. C22⋊C8×C127 | C22 | semidirect |
| 90. C2×C127 | #481 | semidirect |
| 96. C127 | C2×#481 | semidirect |
| 102. C2×C22⋊C8 | D127 | semidirect |
| 118. C22⋊C8 | C2×D127 | semidirect |
| 187. C2 | #22550195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861183 | 2 |
| C22×C4⋊Dic127 | 2 |
| #22550195 | 2 |
| C2×#16861141 | 2 |
| C2×#16861131 | 2 |
| C2×C22⋊C8×C127 | 2 |
| C2×#481 | 127 |