Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22553662 | C2 | semidirect |
| 4. #22553059 | C2 | semidirect |
| 5. Q8⋊(C131⋊C8) | C2 | semidirect |
| 7. #477×C131 | C2 | semidirect |
| 90. C131 | #1637 | semidirect |
| 94. #477 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D524 | 2 |
| #22553662 | 2 |
| #22553599 | 2 |
| #22553059 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553039 | 2 |
| #477×C131 | 2 |
| #1637 | 131 |