Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 2. #22550226 | C2 | semidirect |
| 3. #22550209 | C2 | semidirect |
| 4. #22550171 | C2 | semidirect |
| 5. #22550115 | C2 | semidirect |
| 6. #22550083 | C2 | semidirect |
| 7. #22550032 | C2 | semidirect |
| 8. C4×#14523238 | C2 | semidirect |
| 10. C2×#16861133 | C2 | semidirect |
| 92. D4×C127 | Q16 | semidirect |
| 123. C127 | #3299 | semidirect |
| 208. D4 | #14523238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550583 | 2 |
| #22550226 | 2 |
| #22550209 | 2 |
| #22550171 | 2 |
| #22550115 | 2 |
| #22550083 | 2 |
| #22550032 | 2 |
| C4×#14523238 | 2 |
| D4×C127⋊C8 | 2 |
| C2×#16861133 | 2 |
| D4×Q8×C127 | 2 |
| #3299 | 127 |