Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
432 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 297 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. Q8×C131⋊C8 | C2 | semidirect |
| 2. D4×C131⋊C8 | C2 | semidirect |
| 3. #22553365 | C2 | semidirect |
| 4. C2×C4⋊(C131⋊C8) | C2 | semidirect |
| 22. #41×C131 | C8 | semidirect |
| 38. Q8×C131 | C2×C8 | semidirect |
| 39. D4×C131 | C2×C8 | semidirect |
| 43. C2×C4×C131 | C2×C8 | semidirect |
| 65. C131 | #2988 | semidirect |
| 85. #41 | C131⋊C8 | semidirect |
| 102. Q8 | C2×C131⋊C8 | semidirect |
| 103. D4 | C2×C131⋊C8 | semidirect |
| 107. C2×C4 | C2×C131⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C131⋊C8 | 2 |
| D4×C131⋊C8 | 2 |
| #22553365 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C4×#41×C131 | 2 |
| #2988 | 131 |