Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16861231 | C2 | semidirect |
| 2. C22×C8×D127 | C2 | semidirect |
| 3. #22550388 | C2 | semidirect |
| 4. #22550118 | C2 | semidirect |
| 5. #22550113 | C2 | semidirect |
| 6. #22550106 | C2 | semidirect |
| 7. #22549870 | C2 | semidirect |
| 8. #427×C127 | C2 | semidirect |
| 12. C2×Dic508 | C22 | semidirect |
| 13. C2×#14523237 | C22 | semidirect |
| 14. C2×D1016 | C22 | semidirect |
| 24. #16861132 | C22 | semidirect |
| 25. #16861129 | C22 | semidirect |
| 28. #107×C127 | C22 | semidirect |
| 29. #106×C127 | C22 | semidirect |
| 54. C2×C8×C127 | D4 | semidirect |
| 94. C2×D127 | #135 | semidirect |
| 107. C127 | #3050 | semidirect |
| 114. #427 | D127 | semidirect |
| 133. #107 | C2×D127 | semidirect |
| 134. #106 | C2×D127 | semidirect |
| 158. C2×C8 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| C22×C8×D127 | 2 |
| #22550388 | 2 |
| #22550118 | 2 |
| #22550113 | 2 |
| #22550106 | 2 |
| #22549870 | 2 |
| #427×C127 | 2 |
| #3050 | 127 |