Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 1. C2×#16861241 | C2 | semidirect |
| 2. C2×#16861238 | C2 | semidirect |
| 4. C4⋊Q8×D127 | C2 | semidirect |
| 5. #22550271 | C2 | semidirect |
| 6. #22550270 | C2 | semidirect |
| 7. #22550268 | C2 | semidirect |
| 8. #22550254 | C2 | semidirect |
| 9. #22550247 | C2 | semidirect |
| 10. #22549828 | C2 | semidirect |
| 11. #497×C127 | C2 | semidirect |
| 63. #14523231 | D4 | semidirect |
| 124. Dic127 | #137 | semidirect |
| 131. C127 | #3152 | semidirect |
| 139. #497 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861241 | 2 |
| C2×#16861238 | 2 |
| #22550425 | 2 |
| C4⋊Q8×D127 | 2 |
| #22550271 | 2 |
| #22550270 | 2 |
| #22550268 | 2 |
| #22550254 | 2 |
| #22550247 | 2 |
| #22549828 | 2 |
| #497×C127 | 2 |
| #3152 | 127 |