Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
216 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22553365 | C2 | semidirect |
| 2. #22553336 | C2 | semidirect |
| 3. Q8⋊(C131⋊C8) | C2 | semidirect |
| 4. D4⋊(C131⋊C8) | C2 | semidirect |
| 93. C131 | #1495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553365 | 2 |
| #22553336 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| D4⋊(C131⋊C8) | 2 |
| #529×C131 | 2 |
| #1495 | 131 |