Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
856 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×#14523232 | C2 | semidirect |
| 2. C22×C4×Dic127 | C2 | semidirect |
| 3. C2×#16861136 | C2 | direct (N × H) |
| 7. C2×#14523232 | C22 | semidirect |
| 10. C2×C4×Dic127 | C22 | semidirect |
| 11. #16861136 | C22 | direct (N × H) |
| 14. C2×#41×C127 | C4 | semidirect |
| 16. C22×Q8×C127 | C4 | semidirect |
| 18. C22×D4×C127 | C4 | semidirect |
| 24. #14523232 | C23 | semidirect |
| 27. C4×Dic127 | C23 | semidirect |
| 33. #41×C127 | C2×C4 | semidirect |
| 36. C2×Q8×C127 | C2×C4 | semidirect |
| 40. C2×D4×C127 | C2×C4 | semidirect |
| 60. Q8×C127 | C22×C4 | semidirect |
| 64. D4×C127 | C22×C4 | semidirect |
| 81. C22×C127 | #104 | semidirect |
| 94. C2×C127 | C2×#104 | semidirect |
| 97. C127 | C22×#104 | semidirect |
| 104. C2×#41 | Dic127 | semidirect |
| 106. C22×Q8 | Dic127 | semidirect |
| 108. C22×D4 | Dic127 | semidirect |
| 123. #41 | C2×Dic127 | semidirect |
| 126. C2×Q8 | C2×Dic127 | semidirect |
| 130. C2×D4 | C2×Dic127 | semidirect |
| 154. Q8 | C22×Dic127 | semidirect |
| 158. D4 | C22×Dic127 | semidirect |
| 178. C22 | #16861136 | direct (N × H) |
| 191. C2 | C2×#16861136 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523232 | 2 |
| C22×C4×Dic127 | 2 |
| C2×#16861136 | 2 |
| C22×#41×C127 | 2 |
| C22×#104 | 127 |