Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 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 |
|---|---|---|
| 3. #22553075 | C2 | semidirect |
| 4. #22553074 | C2 | semidirect |
| 5. #340×C131 | C2 | semidirect |
| 10. C2×C8×D131 | C4 | semidirect |
| 14. C4⋊C4×D131 | C4 | semidirect |
| 28. C2×C131⋊C8 | C2×C4 | semidirect |
| 31. C4⋊Dic131 | C2×C4 | semidirect |
| 36. C2×C8×C131 | C2×C4 | semidirect |
| 38. C4⋊C4×C131 | C2×C4 | semidirect |
| 84. D131 | #340 | direct (N × H) |
| 85. C131 | C2×#340 | semidirect |
| 91. #340 | D131 | direct (N × H) |
| 119. C2×C8 | C4×D131 | semidirect |
| 124. C4⋊C4 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D131 | 2 |
| C2×C4⋊C4×D131 | 2 |
| #22553075 | 2 |
| #22553074 | 2 |
| #340×C131 | 2 |
| C2×#340 | 131 |