Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. C2×Q16×D127 | C2 | semidirect |
| 3. #22550315 | C2 | direct (N × H) |
| 4. C2×Dic1016 | C2 | semidirect |
| 5. C2×#16861155 | C2 | semidirect |
| 6. C2×#16861153 | C2 | semidirect |
| 7. C2×#16861148 | C2 | semidirect |
| 8. C2×SD32×C127 | C2 | semidirect |
| 17. Q16×D127 | C22 | semidirect |
| 20. Dic1016 | C22 | semidirect |
| 21. #16861155 | C22 | semidirect |
| 22. #16861153 | C22 | semidirect |
| 23. #16861148 | C22 | semidirect |
| 27. SD32×C127 | C22 | semidirect |
| 94. C2×C127 | #510 | semidirect |
| 98. C127 | C2×#510 | semidirect |
| 105. C2×SD32 | D127 | semidirect |
| 123. SD32 | C2×D127 | semidirect |
| 193. C2 | #22550315 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861228 | 2 |
| C2×Q16×D127 | 2 |
| #22550315 | 2 |
| C2×Dic1016 | 2 |
| C2×#16861155 | 2 |
| C2×#16861153 | 2 |
| C2×#16861148 | 2 |
| C2×SD32×C127 | 2 |
| C2×#510 | 127 |