Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #22550599 | C2 | semidirect |
| 2. #22550238 | C2 | semidirect |
| 3. #22550228 | C2 | semidirect |
| 4. #22550168 | C2 | semidirect |
| 5. #22550153 | C2 | semidirect |
| 7. #22550081 | C2 | semidirect |
| 8. #22550007 | C2 | semidirect |
| 9. #22549976 | C2 | semidirect |
| 11. D4×Q8×C127 | C2 | semidirect |
| 123. C127 | #3367 | semidirect |
| 125. D4×Q8 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550599 | 2 |
| #22550238 | 2 |
| #22550228 | 2 |
| #22550168 | 2 |
| #22550153 | 2 |
| #22550091 | 2 |
| #22550081 | 2 |
| #22550007 | 2 |
| #22549976 | 2 |
| C4×#14523233 | 2 |
| D4×Q8×C127 | 2 |
| #3367 | 127 |