Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. #22549637 | C2 | semidirect |
| 5. #22549636 | C2 | semidirect |
| 6. #22549635 | C2 | semidirect |
| 7. #339×C127 | C2 | semidirect |
| 12. M16×D127 | C4 | semidirect |
| 15. #16861167 | C4 | semidirect |
| 18. #16861166 | C4 | semidirect |
| 21. C4⋊C4×D127 | C4 | semidirect |
| 42. #14523232 | C2×C4 | semidirect |
| 55. C4×Dic127 | C2×C4 | semidirect |
| 59. M16×C127 | C2×C4 | semidirect |
| 65. C42×C127 | C2×C4 | semidirect |
| 126. C127 | #1733 | semidirect |
| 133. #339 | D127 | semidirect |
| 173. M16 | C4×D127 | semidirect |
| 191. C42 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D127 | 2 |
| C2×#16861166 | 2 |
| #117×D127 | 2 |
| #22549637 | 2 |
| #22549636 | 2 |
| #22549635 | 2 |
| #339×C127 | 2 |
| #1733 | 127 |