Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×#16861174 | C2 | semidirect |
| 4. #22549967 | C2 | direct (N × H) |
| 5. C2×#16861140 | C2 | semidirect |
| 6. C2×#16861134 | C2 | semidirect |
| 7. C2×C8×Dic127 | C2 | semidirect |
| 11. C2×#14523236 | C4 | semidirect |
| 15. #16861174 | C22 | semidirect |
| 23. #16861140 | C22 | semidirect |
| 24. #16861134 | C22 | semidirect |
| 25. C8×Dic127 | C22 | semidirect |
| 32. C2×Dic254 | C2×C4 | semidirect |
| 40. #14523236 | C2×C4 | semidirect |
| 41. C2×C127⋊C8 | C2×C4 | semidirect |
| 63. Dic254 | C22×C4 | semidirect |
| 70. C2×Dic127 | SD16 | semidirect |
| 73. C127⋊C8 | C22×C4 | semidirect |
| 104. Dic127 | C2×SD16 | semidirect |
| 106. C2×C127 | C4×SD16 | semidirect |
| 111. C127 | C2×C4×SD16 | semidirect |
| 217. C2 | #22549967 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523236 | 2 |
| C2×#16861174 | 2 |
| C2×D4×Dic127 | 2 |
| #22549967 | 2 |
| C2×#16861140 | 2 |
| C2×#16861134 | 2 |
| C2×C8×Dic127 | 2 |
| C2×#102×C127 | 2 |
| C2×C4×SD16 | 127 |