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. #22550309 | C2 | direct (N × H) |
| 3. C2×#16861152 | C2 | semidirect |
| 4. C2×D2032 | C2 | semidirect |
| 5. C2×C16×D127 | C2 | semidirect |
| 6. C2×Q32×C127 | C2 | semidirect |
| 9. #16861232 | C22 | semidirect |
| 13. #16861152 | C22 | semidirect |
| 14. D2032 | C22 | semidirect |
| 16. C16×D127 | C22 | semidirect |
| 18. Q32×C127 | C22 | semidirect |
| 63. C2×C127 | #508 | semidirect |
| 68. C127 | C2×#508 | semidirect |
| 71. C2×Q32 | D127 | semidirect |
| 82. Q32 | C2×D127 | semidirect |
| 133. C2 | #22550309 | 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 |
| #22550309 | 2 |
| C2×#16861152 | 2 |
| C2×D2032 | 2 |
| C2×C16×D127 | 2 |
| C2×Q32×C127 | 2 |
| C2×#508 | 127 |