Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
284 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 9. C4⋊Q8×C127 | C4 | semidirect |
| 10. #125×C127 | C4 | semidirect |
| 20. C4×Dic127 | Q8 | semidirect |
| 59. C127 | #1994 | semidirect |
| 65. C4⋊Q8 | Dic127 | semidirect |
| 66. #125 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549900 | 2 |
| C42×Dic127 | 2 |
| #22549635 | 2 |
| #533×C127 | 2 |
| #1994 | 127 |