Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22550548 | C2 | semidirect |
| 3. #22550253 | C2 | semidirect |
| 4. #22550113 | C2 | semidirect |
| 5. #22550076 | C2 | semidirect |
| 6. #22550024 | C2 | semidirect |
| 7. C8×D508 | C2 | semidirect |
| 8. C4×Q16×C127 | C2 | semidirect |
| 48. Q16×C127 | D4 | semidirect |
| 88. C4×C127 | #135 | semidirect |
| 98. C127 | #3287 | semidirect |
| 105. C4×Q16 | D127 | semidirect |
| 138. Q16 | D508 | semidirect |
| 187. C4 | #16861232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| #22550548 | 2 |
| #22550253 | 2 |
| #22550113 | 2 |
| #22550076 | 2 |
| #22550024 | 2 |
| C8×D508 | 2 |
| C4×Q16×C127 | 2 |
| #3287 | 127 |