Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
224 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×C16×D127 | C2 | semidirect |
| 3. #108×D127 | C2 | semidirect |
| 4. #22549684 | C2 | semidirect |
| 5. #22549683 | C2 | semidirect |
| 6. #22549682 | C2 | semidirect |
| 7. #359×C127 | C2 | semidirect |
| 19. C2×C127⋊C16 | C22 | semidirect |
| 22. #16861145 | C22 | semidirect |
| 25. C2×C16×C127 | C22 | semidirect |
| 26. #108×C127 | C22 | semidirect |
| 107. D127 | #359 | direct (N × H) |
| 109. C127 | C2×#359 | semidirect |
| 116. #359 | D127 | direct (N × H) |
| 132. C2×C16 | C2×D127 | semidirect |
| 135. #108 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D127 | 2 |
| C2×C16×D127 | 2 |
| #108×D127 | 2 |
| #22549684 | 2 |
| #22549683 | 2 |
| #22549682 | 2 |
| #359×C127 | 2 |
| C2×#359 | 127 |