Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22549975 | C2 | direct (N × H) |
| 5. C2×#16861132 | C2 | semidirect |
| 7. C2×#16861119 | C2 | semidirect |
| 8. C2×#107×C127 | C2 | semidirect |
| 12. C2×#14523237 | C4 | semidirect |
| 16. #16861174 | C22 | semidirect |
| 23. #16861132 | C22 | semidirect |
| 25. #16861119 | C22 | semidirect |
| 29. #107×C127 | C22 | semidirect |
| 33. C2×Dic254 | C2×C4 | semidirect |
| 44. #14523237 | C2×C4 | semidirect |
| 55. C2×C8×C127 | C2×C4 | semidirect |
| 67. Dic254 | C22×C4 | semidirect |
| 88. C8×C127 | C22×C4 | semidirect |
| 105. C2×C127 | #440 | semidirect |
| 111. C127 | C2×#440 | semidirect |
| 116. C2×#107 | D127 | semidirect |
| 137. #107 | C2×D127 | semidirect |
| 161. C2×C8 | C4×D127 | semidirect |
| 199. C8 | C2×C4×D127 | semidirect |
| 217. C2 | #22549975 | 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×#16861174 | 2 |
| C2×#16861171 | 2 |
| #22549975 | 2 |
| C2×#16861132 | 2 |
| C2×#16861129 | 2 |
| C2×#16861119 | 2 |
| C2×#107×C127 | 2 |
| C2×#440 | 127 |