Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #22550317 | C2 | direct (N × H) |
| 3. C2×#16861155 | C2 | semidirect |
| 4. C2×#16861152 | C2 | semidirect |
| 5. C2×#16861149 | C2 | semidirect |
| 6. C22×Q16×C127 | C2 | semidirect |
| 13. #16861155 | C22 | semidirect |
| 14. #16861152 | C22 | semidirect |
| 15. #16861149 | C22 | semidirect |
| 21. C2×Q16×C127 | C22 | semidirect |
| 80. C2×C127 | #510 | semidirect |
| 84. C127 | C2×#510 | semidirect |
| 86. C22×Q16 | D127 | semidirect |
| 99. C2×Q16 | C2×D127 | semidirect |
| 165. C2 | #22550317 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| #22550317 | 2 |
| C2×#16861155 | 2 |
| C2×#16861152 | 2 |
| C2×#16861149 | 2 |
| C22×Q16×C127 | 2 |
| C2×#510 | 127 |