Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
344 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C4⋊(C131⋊C8) | C2 | semidirect |
| 2. C2×C4×C131⋊C8 | C2 | semidirect |
| 3. D4⋊(C131⋊C8) | C2 | direct (N × H) |
| 8. C4⋊(C131⋊C8) | C22 | semidirect |
| 10. C4×C131⋊C8 | C22 | semidirect |
| 27. C2×D4×C131 | C8 | semidirect |
| 54. D4×C131 | C2×C8 | semidirect |
| 89. C2×C131 | D4⋊C8 | semidirect |
| 93. C131 | C2×D4⋊C8 | semidirect |
| 117. C2×D4 | C131⋊C8 | semidirect |
| 146. D4 | C2×C131⋊C8 | semidirect |
| 183. C2 | D4⋊(C131⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C131⋊C8) | 2 |
| C2×C4×C131⋊C8 | 2 |
| D4⋊(C131⋊C8) | 2 |
| C2×C4×D4×C131 | 2 |
| C2×D4⋊C8 | 131 |