Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×Q16×D127 | C2 | semidirect |
| 3. #22550538 | C2 | semidirect |
| 4. #22550260 | C2 | semidirect |
| 5. #22550118 | C2 | semidirect |
| 6. #22550113 | C2 | semidirect |
| 7. #22550098 | C2 | semidirect |
| 8. #22550041 | C2 | semidirect |
| 9. #22550016 | C2 | semidirect |
| 10. C8×D508 | C2 | semidirect |
| 11. C4×Q16×C127 | C2 | semidirect |
| 73. Q16×C127 | D4 | semidirect |
| 120. C2×D127 | #135 | semidirect |
| 137. C127 | #3285 | semidirect |
| 147. C4×Q16 | D127 | semidirect |
| 195. Q16 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861232 | 2 |
| C2×Q16×D127 | 2 |
| #22550538 | 2 |
| #22550260 | 2 |
| #22550118 | 2 |
| #22550113 | 2 |
| #22550098 | 2 |
| #22550041 | 2 |
| #22550016 | 2 |
| C8×D508 | 2 |
| C4×Q16×C127 | 2 |
| #3285 | 127 |