Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16861232 | C2 | semidirect |
| 2. C2×#16861228 | C2 | semidirect |
| 3. #22550307 | C2 | direct (N × H) |
| 4. C2×#16861155 | C2 | semidirect |
| 5. C2×#16861154 | C2 | semidirect |
| 6. C2×#16861150 | C2 | semidirect |
| 7. C2×C16×D127 | C2 | semidirect |
| 8. C2×SD32×C127 | C2 | semidirect |
| 12. #16861232 | C22 | semidirect |
| 14. #16861228 | C22 | semidirect |
| 20. #16861155 | C22 | semidirect |
| 21. #16861154 | C22 | semidirect |
| 22. #16861150 | C22 | semidirect |
| 24. C16×D127 | C22 | semidirect |
| 27. SD32×C127 | C22 | semidirect |
| 95. C2×C127 | #508 | semidirect |
| 100. C127 | C2×#508 | semidirect |
| 106. C2×SD32 | D127 | semidirect |
| 124. SD32 | C2×D127 | semidirect |
| 197. C2 | #22550307 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| C2×#16861228 | 2 |
| #22550307 | 2 |
| C2×#16861155 | 2 |
| C2×#16861154 | 2 |
| C2×#16861150 | 2 |
| C2×C16×D127 | 2 |
| C2×SD32×C127 | 2 |
| C2×#508 | 127 |