Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22553717 | C2 | semidirect |
| 3. #22553597 | C2 | semidirect |
| 5. #22553059 | C2 | semidirect |
| 7. Q8⋊C8×C131 | C2 | semidirect |
| 88. C131 | #1650 | semidirect |
| 95. Q8⋊C8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554035 | 2 |
| #22553717 | 2 |
| #22553597 | 2 |
| #22553518 | 2 |
| #22553059 | 2 |
| #22553041 | 2 |
| Q8⋊C8×C131 | 2 |
| #1650 | 131 |