Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 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 |
|---|---|---|
| 3. #22549750 | C2 | semidirect |
| 4. #22549747 | C2 | semidirect |
| 5. #22549736 | C2 | semidirect |
| 6. #22549734 | C2 | semidirect |
| 7. #380×C127 | C2 | semidirect |
| 11. C2×C4⋊Dic127 | C22 | semidirect |
| 12. C2×Dic127⋊C4 | C22 | semidirect |
| 14. C2×(C2×D127)⋊C4 | C4 | semidirect |
| 19. C127⋊#95 | C22 | semidirect |
| 20. C127⋊#95 | C22 | semidirect |
| 22. C2×C4⋊C4×C127 | C22 | semidirect |
| 24. #95×C127 | C22 | semidirect |
| 32. C22×Dic127 | C2×C4 | semidirect |
| 42. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 43. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 46. C22×C4×C127 | C2×C4 | semidirect |
| 58. C22×D127 | C4⋊C4 | semidirect |
| 112. C127 | #2315 | semidirect |
| 119. #380 | D127 | semidirect |
| 126. C2×C4⋊C4 | C2×D127 | semidirect |
| 136. #95 | C2×D127 | semidirect |
| 152. C22×C4 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D127)⋊C4 | 2 |
| C2×C22⋊C4×D127 | 2 |
| #22549750 | 2 |
| #22549747 | 2 |
| #22549736 | 2 |
| #22549734 | 2 |
| #380×C127 | 2 |
| #2315 | 127 |