Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 221 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. #22550359 | C2 | semidirect |
| 2. #22549988 | C2 | semidirect |
| 3. #22549983 | C2 | semidirect |
| 4. SD16×Dic127 | C2 | semidirect |
| 5. C2×#16861141 | C2 | semidirect |
| 6. #22549877 | C2 | semidirect |
| 7. #22549831 | C2 | semidirect |
| 24. #135×C127 | C4 | semidirect |
| 42. #41×C127 | C2×C4 | semidirect |
| 48. Q16×C127 | C2×C4 | semidirect |
| 49. SD16×C127 | C2×C4 | semidirect |
| 50. D8×C127 | C2×C4 | semidirect |
| 51. C2×C8×C127 | C2×C4 | semidirect |
| 91. C127 | #2952 | semidirect |
| 101. #135 | Dic127 | semidirect |
| 121. #41 | C2×Dic127 | semidirect |
| 129. Q16 | C2×Dic127 | semidirect |
| 130. SD16 | C2×Dic127 | semidirect |
| 131. D8 | C2×Dic127 | semidirect |
| 134. C2×C8 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550359 | 2 |
| #22549988 | 2 |
| #22549983 | 2 |
| SD16×Dic127 | 2 |
| C2×#16861141 | 2 |
| #22549877 | 2 |
| #22549831 | 2 |
| C2×#135×C127 | 2 |
| #2952 | 127 |