Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22553660 | C2 | semidirect |
| 3. #22553599 | C2 | semidirect |
| 4. #22553512 | C2 | semidirect |
| 5. Q8×C131⋊C8 | C2 | semidirect |
| 6. C4×#14523500 | C2 | semidirect |
| 7. Q82×C131 | C2 | semidirect |
| 54. Q8×C131 | SD16 | semidirect |
| 55. Q8×C131 | #41 | semidirect |
| 76. C131 | #3362 | semidirect |
| 78. Q82 | D131 | semidirect |
| 123. Q8 | #14523500 | semidirect |
| 124. Q8 | #14523514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553984 | 2 |
| #22553660 | 2 |
| #22553599 | 2 |
| #22553512 | 2 |
| Q8×C131⋊C8 | 2 |
| C4×#14523500 | 2 |
| Q82×C131 | 2 |
| #3362 | 131 |