Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
168 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #22553062 | C2 | semidirect |
| 4. Q8⋊(C131⋊C8) | C2 | semidirect |
| 6. #22553033 | C2 | semidirect |
| 7. #446×C131 | C2 | semidirect |
| 60. C8×C131 | SD16 | semidirect |
| 77. C131 | #1582 | semidirect |
| 79. #446 | D131 | semidirect |
| 138. C8 | #14523500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523500 | 2 |
| C8×D524 | 2 |
| #22553062 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553039 | 2 |
| #22553033 | 2 |
| #446×C131 | 2 |
| #1582 | 131 |