Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22549903 | C2 | semidirect |
| 4. C2×#16861119 | C2 | semidirect |
| 5. #22549641 | C2 | semidirect |
| 6. #22549635 | C2 | semidirect |
| 19. #103×C127 | C4 | semidirect |
| 20. #102×C127 | C4 | semidirect |
| 91. C127 | #1938 | semidirect |
| 108. #103 | Dic127 | semidirect |
| 109. #102 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549903 | 2 |
| C2×#16861136 | 2 |
| #22549843 | 2 |
| C2×#16861119 | 2 |
| #22549641 | 2 |
| #22549635 | 2 |
| #416×C127 | 2 |
| #1938 | 127 |