Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1624 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 725 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 |
|---|---|---|
| 2. C2×#16862245 | C2 | direct (N × H) |
| 12. #16862245 | C22 | direct (N × H) |
| 23. C22×Dic131 | Q8 | semidirect |
| 32. C22×C4×C131 | Q8 | semidirect |
| 39. C2×Dic131 | C2×Q8 | semidirect |
| 48. C2×C4×C131 | C2×Q8 | semidirect |
| 51. C22×C131 | C4⋊Q8 | semidirect |
| 57. C4×C131 | C22×Q8 | semidirect |
| 60. Dic131 | C22×Q8 | semidirect |
| 61. C2×C131 | C2×C4⋊Q8 | semidirect |
| 65. C131 | C22×C4⋊Q8 | semidirect |
| 95. C22×C4 | Dic262 | semidirect |
| 114. C2×C4 | C2×Dic262 | semidirect |
| 117. C22 | #16862245 | direct (N × H) |
| 126. C4 | C22×Dic262 | semidirect |
| 127. C2 | C2×#16862245 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic262 | 2 |
| C2×#16862245 | 2 |
| C22×C4⋊Dic131 | 2 |
| C22×Dic131⋊C4 | 2 |
| C22×C4×Dic131 | 2 |
| C22×C4⋊C4×C131 | 2 |
| C22×C4⋊Q8 | 131 |