Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 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 |
|---|---|---|
| 4. #22549915 | C2 | direct (N × H) |
| 5. C2×#16861143 | C2 | semidirect |
| 6. C2×#16861142 | C2 | semidirect |
| 7. C2×#16861140 | C2 | semidirect |
| 8. C2×#106×C127 | C2 | semidirect |
| 11. C2×#14523231 | C4 | semidirect |
| 23. #16861143 | C22 | semidirect |
| 24. #16861142 | C22 | semidirect |
| 25. #16861140 | C22 | semidirect |
| 29. #106×C127 | C22 | semidirect |
| 40. #14523231 | C2×C4 | semidirect |
| 41. C2×C127⋊C8 | C2×C4 | semidirect |
| 53. C2×C8×C127 | C2×C4 | semidirect |
| 73. C127⋊C8 | C22×C4 | semidirect |
| 83. C8×C127 | C22×C4 | semidirect |
| 100. C2×C127 | #428 | semidirect |
| 106. C127 | C2×#428 | semidirect |
| 114. C2×#106 | D127 | semidirect |
| 135. #106 | C2×D127 | semidirect |
| 152. C2×C8 | C4×D127 | semidirect |
| 189. C8 | C2×C4×D127 | semidirect |
| 207. C2 | #22549915 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523231 | 2 |
| C2×#16861167 | 2 |
| C2×C4⋊C4×D127 | 2 |
| #22549915 | 2 |
| C2×#16861143 | 2 |
| C2×#16861142 | 2 |
| C2×#16861140 | 2 |
| C2×#106×C127 | 2 |
| C2×#428 | 127 |