Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #22550242 | C2 | semidirect |
| 3. #22550224 | C2 | semidirect |
| 4. #22550173 | C2 | semidirect |
| 5. #22550153 | C2 | semidirect |
| 6. #22550076 | C2 | semidirect |
| 7. #22550076 | C2 | semidirect |
| 8. #22550007 | C2 | semidirect |
| 9. #22549974 | C2 | semidirect |
| 10. C4×#14523235 | C2 | semidirect |
| 11. #557×C127 | C2 | semidirect |
| 93. Q8×C127 | #41 | semidirect |
| 125. C127 | #3368 | semidirect |
| 126. #557 | D127 | semidirect |
| 204. Q8 | #14523249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550548 | 2 |
| #22550242 | 2 |
| #22550224 | 2 |
| #22550173 | 2 |
| #22550153 | 2 |
| #22550076 | 2 |
| #22550007 | 2 |
| #22549974 | 2 |
| C4×#14523235 | 2 |
| #557×C127 | 2 |
| #3368 | 127 |