Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
232 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22549916 | C2 | semidirect |
| 5. #22549834 | C2 | semidirect |
| 6. #22549640 | C2 | semidirect |
| 7. #343×C127 | C2 | semidirect |
| 18. #16861125 | C4 | semidirect |
| 101. C127 | #1931 | semidirect |
| 107. #343 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549916 | 2 |
| #22549882 | 2 |
| C2×#16861129 | 2 |
| C2×#16861125 | 2 |
| #22549834 | 2 |
| #22549640 | 2 |
| #343×C127 | 2 |
| #1931 | 127 |