Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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×#16861143 | C2 | semidirect |
| 4. C2×#16861142 | C2 | semidirect |
| 5. #107×D127 | C2 | direct (N × H) |
| 6. C2×#107×C127 | C2 | semidirect |
| 10. C2×C8×D127 | C4 | semidirect |
| 16. #16861143 | C22 | semidirect |
| 17. #16861142 | C22 | semidirect |
| 20. #107×C127 | C22 | semidirect |
| 30. C2×C127⋊C8 | C2×C4 | semidirect |
| 32. C8×D127 | C2×C4 | semidirect |
| 38. C2×C8×C127 | C2×C4 | semidirect |
| 54. C127⋊C8 | C22×C4 | semidirect |
| 62. C8×C127 | C22×C4 | semidirect |
| 67. C2×D127 | #107 | direct (N × H) |
| 77. C2×C127 | C2×#107 | semidirect |
| 81. D127 | C2×#107 | direct (N × H) |
| 83. C127 | C22×#107 | semidirect |
| 89. C2×#107 | D127 | direct (N × H) |
| 103. #107 | C2×D127 | direct (N × H) |
| 118. C2×C8 | C4×D127 | semidirect |
| 145. C8 | C2×C4×D127 | semidirect |
| 161. C2 | #107×D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D127 | 2 |
| C2×C4⋊C4×D127 | 2 |
| C2×#16861143 | 2 |
| C2×#16861142 | 2 |
| #107×D127 | 2 |
| C2×#107×C127 | 2 |
| C22×#107 | 127 |