Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16861230 | C2 | semidirect |
| 3. C2×#16861228 | C2 | semidirect |
| 4. #22550425 | C2 | semidirect |
| 5. #22550260 | C2 | semidirect |
| 6. #22550258 | C2 | semidirect |
| 7. #22550254 | C2 | semidirect |
| 8. #22550251 | C2 | semidirect |
| 9. #22550247 | C2 | semidirect |
| 10. C4×C8×D127 | C2 | semidirect |
| 11. #495×C127 | C2 | semidirect |
| 62. C8×D127 | D4 | semidirect |
| 63. C8×D127 | D4 | semidirect |
| 119. Dic127 | #135 | semidirect |
| 126. C127 | #3147 | semidirect |
| 133. #495 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| C2×#16861230 | 2 |
| C2×#16861228 | 2 |
| #22550425 | 2 |
| #22550260 | 2 |
| #22550258 | 2 |
| #22550254 | 2 |
| #22550251 | 2 |
| #22550247 | 2 |
| C4×C8×D127 | 2 |
| #495×C127 | 2 |
| #3147 | 127 |