Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×C4×Dic254 | C2 | semidirect |
| 4. C4×#14523237 | C2 | direct (N × H) |
| 5. C2×#16861141 | C2 | semidirect |
| 6. C2×#16861134 | C2 | semidirect |
| 8. C2×C4×C8×C127 | C2 | semidirect |
| 12. C2×#14523237 | C4 | direct (N × H) |
| 15. C4×Dic254 | C22 | semidirect |
| 23. #16861141 | C22 | semidirect |
| 24. #16861134 | C22 | semidirect |
| 29. C4×C8×C127 | C22 | semidirect |
| 33. C2×Dic254 | C2×C4 | semidirect |
| 44. #14523237 | C2×C4 | direct (N × H) |
| 56. C2×C8×C127 | C2×C4 | semidirect |
| 67. Dic254 | C22×C4 | semidirect |
| 80. C2×C4×C127 | SD16 | semidirect |
| 88. C8×C127 | C22×C4 | semidirect |
| 99. C4×C127 | C2×SD16 | semidirect |
| 105. C2×C127 | C4×SD16 | semidirect |
| 111. C127 | C2×C4×SD16 | semidirect |
| 119. C2×C4×C8 | D127 | semidirect |
| 140. C4×C8 | C2×D127 | semidirect |
| 160. C2×C8 | C4×D127 | semidirect |
| 191. C2×C4 | #14523237 | direct (N × H) |
| 199. C8 | C2×C4×D127 | semidirect |
| 213. C4 | C2×#14523237 | direct (N × H) |
| 217. C2 | C4×#14523237 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523237 | 2 |
| C2×C4×Dic254 | 2 |
| C2×C4×D508 | 2 |
| C4×#14523237 | 2 |
| C2×#16861141 | 2 |
| C2×#16861134 | 2 |
| C2×#16861131 | 2 |
| C2×C4×C8×C127 | 2 |
| C2×C4×SD16 | 127 |