Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22550548 | C2 | semidirect |
| 2. #22550224 | C2 | semidirect |
| 3. #22550153 | C2 | semidirect |
| 4. #22550071 | C2 | semidirect |
| 5. Q8×C127⋊C8 | C2 | semidirect |
| 6. C4×#14523233 | C2 | semidirect |
| 7. D4×Q8×C127 | C2 | semidirect |
| 55. Q8×C127 | D8 | semidirect |
| 57. D4×C127 | #41 | semidirect |
| 82. C127 | #3358 | semidirect |
| 84. D4×Q8 | D127 | semidirect |
| 129. Q8 | #14523233 | semidirect |
| 135. D4 | #14523249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550548 | 2 |
| #22550224 | 2 |
| #22550153 | 2 |
| #22550071 | 2 |
| Q8×C127⋊C8 | 2 |
| C4×#14523233 | 2 |
| D4×Q8×C127 | 2 |
| #3358 | 127 |