Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 3. #22549703 | C2 | semidirect |
| 4. #22549681 | C2 | semidirect |
| 5. #22549679 | C2 | semidirect |
| 7. #366×C127 | C2 | semidirect |
| 66. C127 | #2237 | semidirect |
| 70. #366 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550118 | 2 |
| #22549913 | 2 |
| #22549703 | 2 |
| #22549681 | 2 |
| #22549679 | 2 |
| (C2×D127)⋊C16 | 2 |
| #366×C127 | 2 |
| #2237 | 127 |