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×#16861229 | C2 | semidirect |
| 2. #22550547 | C2 | semidirect |
| 3. #22550252 | C2 | semidirect |
| 4. #22550110 | C2 | semidirect |
| 5. #22550076 | C2 | semidirect |
| 6. #22550073 | C2 | semidirect |
| 7. #22550021 | C2 | semidirect |
| 8. #22550019 | C2 | semidirect |
| 9. C4×#14523238 | C2 | semidirect |
| 10. D4×C127⋊C8 | C2 | semidirect |
| 11. #550×C127 | C2 | semidirect |
| 51. #14523238 | D4 | semidirect |
| 131. C4×C127 | #135 | semidirect |
| 143. C127 | #3287 | semidirect |
| 146. #550 | D127 | semidirect |
| 276. C4 | #16861229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861229 | 2 |
| #22550547 | 2 |
| #22550252 | 2 |
| #22550110 | 2 |
| #22550076 | 2 |
| #22550073 | 2 |
| #22550021 | 2 |
| #22550019 | 2 |
| C4×#14523238 | 2 |
| D4×C127⋊C8 | 2 |
| #550×C127 | 2 |
| #3287 | 127 |