Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic254 | C2 | semidirect |
| 3. #22550227 | C2 | semidirect |
| 4. #22550207 | C2 | semidirect |
| 5. #22550162 | C2 | semidirect |
| 6. #22550105 | C2 | semidirect |
| 7. #22550082 | C2 | semidirect |
| 8. #22550017 | C2 | semidirect |
| 9. C4×#14523237 | C2 | semidirect |
| 10. C2×#16861134 | C2 | semidirect |
| 11. C8×D4×C127 | C2 | semidirect |
| 83. Dic254 | #41 | semidirect |
| 96. D4×C127 | SD16 | semidirect |
| 129. C127 | #3298 | semidirect |
| 139. C8×D4 | D127 | semidirect |
| 217. D4 | #14523237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic254 | 2 |
| #22550530 | 2 |
| #22550227 | 2 |
| #22550207 | 2 |
| #22550162 | 2 |
| #22550105 | 2 |
| #22550082 | 2 |
| #22550017 | 2 |
| C4×#14523237 | 2 |
| C2×#16861134 | 2 |
| C8×D4×C127 | 2 |
| #3298 | 127 |