Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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. #22549701 | C2 | semidirect |
| 4. #22549681 | C2 | semidirect |
| 5. #22549679 | C2 | semidirect |
| 7. #366×C127 | C2 | semidirect |
| 67. C127 | #2236 | semidirect |
| 71. #366 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550118 | 2 |
| #107×D127 | 2 |
| #22549701 | 2 |
| #22549681 | 2 |
| #22549679 | 2 |
| (C2×D127)⋊C16 | 2 |
| #366×C127 | 2 |
| #2236 | 127 |