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×#16861141 | C2 | semidirect |
| 4. C2×#16861140 | C2 | semidirect |
| 5. #106×D127 | C2 | direct (N × H) |
| 6. C2×#106×C127 | C2 | semidirect |
| 10. C2×C8×D127 | C4 | semidirect |
| 16. #16861141 | C22 | semidirect |
| 17. #16861140 | C22 | semidirect |
| 20. #106×C127 | C22 | semidirect |
| 30. C2×C127⋊C8 | C2×C4 | semidirect |
| 32. C8×D127 | C2×C4 | semidirect |
| 38. C2×C8×C127 | C2×C4 | semidirect |
| 53. C127⋊C8 | C22×C4 | semidirect |
| 61. C8×C127 | C22×C4 | semidirect |
| 65. C2×D127 | #106 | direct (N × H) |
| 74. C2×C127 | C2×#106 | semidirect |
| 77. D127 | C2×#106 | direct (N × H) |
| 79. C127 | C22×#106 | semidirect |
| 85. C2×#106 | D127 | direct (N × H) |
| 99. #106 | C2×D127 | direct (N × H) |
| 114. C2×C8 | C4×D127 | semidirect |
| 140. C8 | C2×C4×D127 | semidirect |
| 154. C2 | #106×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×#16861141 | 2 |
| C2×#16861140 | 2 |
| #106×D127 | 2 |
| C2×#106×C127 | 2 |
| C22×#106 | 127 |