Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 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. #22550354 | C2 | semidirect |
| 3. #22549977 | C2 | semidirect |
| 4. SD16×Dic127 | C2 | semidirect |
| 5. #22549914 | C2 | semidirect |
| 6. #22549885 | C2 | semidirect |
| 8. #22549831 | C2 | semidirect |
| 12. Q8×Dic127 | C22 | semidirect |
| 20. #16861143 | C22 | semidirect |
| 21. #16861141 | C22 | semidirect |
| 22. #16861133 | C22 | semidirect |
| 24. #16861119 | C22 | semidirect |
| 25. C8×Dic127 | C22 | semidirect |
| 28. C2×SD16×C127 | C4 | semidirect |
| 50. C2×Q8×C127 | C2×C4 | semidirect |
| 58. SD16×C127 | C2×C4 | semidirect |
| 59. SD16×C127 | C2×C4 | semidirect |
| 60. C2×C8×C127 | C2×C4 | semidirect |
| 104. C127 | #2949 | semidirect |
| 116. C2×SD16 | Dic127 | semidirect |
| 139. C2×Q8 | C2×Dic127 | semidirect |
| 148. SD16 | C2×Dic127 | semidirect |
| 149. SD16 | C2×Dic127 | semidirect |
| 152. C2×C8 | C2×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550354 | 2 |
| #22550351 | 2 |
| #22549977 | 2 |
| SD16×Dic127 | 2 |
| #22549914 | 2 |
| #22549885 | 2 |
| #22549881 | 2 |
| #22549831 | 2 |
| C22×SD16×C127 | 2 |
| #2949 | 127 |