Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
328 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553038 | C2 | direct (N × H) |
| 24. C22×C4×C131 | C8 | semidirect |
| 54. C2×C4×C131 | C2×C8 | semidirect |
| 76. C2×C131 | #324 | semidirect |
| 80. C131 | C2×#324 | semidirect |
| 103. C22×C4 | C131⋊C8 | semidirect |
| 134. C2×C4 | C2×C131⋊C8 | semidirect |
| 157. C2 | #22553038 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C131⋊C8) | 2 |
| #22553038 | 2 |
| C22×C4⋊C4×C131 | 2 |
| C2×#324 | 131 |