Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #22553044 | C2 | semidirect |
| 5. Q8⋊(C131⋊C8) | C2 | semidirect |
| 6. #22553042 | C2 | semidirect |
| 7. Q8⋊C8×C131 | C2 | semidirect |
| 100. C131 | #1481 | semidirect |
| 108. Q8⋊C8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553866 | 2 |
| #22553363 | 2 |
| C4⋊C8×D131 | 2 |
| #22553044 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553042 | 2 |
| Q8⋊C8×C131 | 2 |
| #1481 | 131 |