Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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. #22549932 | C2 | semidirect |
| 3. #22549928 | C2 | semidirect |
| 4. #22549900 | C2 | semidirect |
| 6. M16×Dic127 | C2 | semidirect |
| 7. #423×C127 | C2 | semidirect |
| 17. C4⋊(C127⋊C8) | C22 | semidirect |
| 19. #16861119 | C22 | semidirect |
| 20. C8×Dic127 | C22 | semidirect |
| 23. C4⋊C8×C127 | C22 | semidirect |
| 66. C4×D127 | M16 | semidirect |
| 97. C127 | #2920 | semidirect |
| 102. #423 | D127 | semidirect |
| 117. C4⋊C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D127 | 2 |
| #22549932 | 2 |
| #22549928 | 2 |
| #22549900 | 2 |
| #22549839 | 2 |
| M16×Dic127 | 2 |
| #423×C127 | 2 |
| #2920 | 127 |