Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
2528 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 685 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. C23×D508 | C2 | semidirect |
| 2. C23×D508 | C2 | semidirect |
| 3. C23×C4×D127 | C2 | semidirect |
| 4. C2×#16861184 | C2 | direct (N × H) |
| 5. C22×(C2×D127)⋊C4 | C2 | semidirect |
| 6. C22×C4⋊C4×C127 | C2 | semidirect |
| 11. C22×D508 | C22 | semidirect |
| 12. C22×D508 | C22 | semidirect |
| 15. C22×C4×D127 | C22 | semidirect |
| 16. #16861184 | C22 | direct (N × H) |
| 17. C2×(C2×D127)⋊C4 | C22 | semidirect |
| 20. C2×C4⋊C4×C127 | C22 | semidirect |
| 26. C23×D127 | D4 | semidirect |
| 31. C2×D508 | C23 | semidirect |
| 32. C2×D508 | C23 | semidirect |
| 36. C2×C4×D127 | C23 | semidirect |
| 37. (C2×D127)⋊C4 | C23 | semidirect |
| 40. C22×C4×C127 | D4 | semidirect |
| 43. C4⋊C4×C127 | C23 | semidirect |
| 51. C22×D127 | C2×D4 | semidirect |
| 64. C2×C4×C127 | C2×D4 | semidirect |
| 67. C22×C127 | #121 | semidirect |
| 79. C2×D127 | C22×D4 | semidirect |
| 81. C4×C127 | C22×D4 | semidirect |
| 83. C2×C127 | C2×#121 | semidirect |
| 90. C127 | C22×#121 | semidirect |
| 95. C22×C4⋊C4 | D127 | semidirect |
| 109. C2×C4⋊C4 | C2×D127 | semidirect |
| 129. C22×C4 | D508 | semidirect |
| 132. C4⋊C4 | C22×D127 | semidirect |
| 154. C2×C4 | C2×D508 | semidirect |
| 165. C22 | #16861184 | direct (N × H) |
| 172. C4 | C22×D508 | semidirect |
| 175. C2 | C2×#16861184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D508 | 2 |
| C23×C4×D127 | 2 |
| C2×#16861184 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C22×#121 | 127 |