Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14523500 | C2 | semidirect |
| 3. #22553686 | C2 | direct (N × H) |
| 4. C2×C4×C131⋊C8 | C2 | semidirect |
| 5. C2×C4⋊Q8×C131 | C2 | semidirect |
| 9. C2×#14523500 | C22 | semidirect |
| 13. C4×C131⋊C8 | C22 | semidirect |
| 16. C4⋊Q8×C131 | C22 | semidirect |
| 26. C2×C131⋊C8 | D4 | semidirect |
| 43. C131⋊C8 | C2×D4 | semidirect |
| 49. C2×C4×C131 | SD16 | semidirect |
| 62. C4×C131 | C2×SD16 | semidirect |
| 64. C2×C131 | #492 | semidirect |
| 68. C131 | C2×#492 | semidirect |
| 71. C2×C4⋊Q8 | D131 | semidirect |
| 82. C4⋊Q8 | C2×D131 | semidirect |
| 117. C2×C4 | #14523500 | semidirect |
| 131. C4 | C2×#14523500 | semidirect |
| 134. C2 | #22553686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523500 | 2 |
| C2×#16862243 | 2 |
| #22553686 | 2 |
| C2×C4×C131⋊C8 | 2 |
| C2×C4⋊Q8×C131 | 2 |
| C2×#492 | 131 |