Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
148 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#16861150 | C2 | semidirect |
| 2. #22550294 | C2 | semidirect |
| 3. #22550147 | C2 | semidirect |
| 4. #22550143 | C2 | semidirect |
| 5. #22549705 | C2 | semidirect |
| 6. #22549690 | C2 | semidirect |
| 7. #361×C127 | C2 | semidirect |
| 74. C127 | #2221 | semidirect |
| 81. #361 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861150 | 2 |
| #22550294 | 2 |
| #22550147 | 2 |
| #22550143 | 2 |
| #22549705 | 2 |
| #22549690 | 2 |
| #361×C127 | 2 |
| #2221 | 127 |