Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #22554041 | C2 | semidirect |
| 3. #22553675 | C2 | semidirect |
| 4. #22553658 | C2 | semidirect |
| 5. #22553610 | C2 | semidirect |
| 6. #22553593 | C2 | semidirect |
| 7. #22553510 | C2 | semidirect |
| 8. #22553439 | C2 | semidirect |
| 9. #22553413 | C2 | semidirect |
| 10. C4×#14523500 | C2 | semidirect |
| 11. #460×C131 | C2 | semidirect |
| 91. Q8×C131 | #41 | semidirect |
| 124. C131 | #3368 | semidirect |
| 133. #460 | D131 | semidirect |
| 204. Q8 | #14523512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554041 | 2 |
| #22553982 | 2 |
| #22553675 | 2 |
| #22553658 | 2 |
| #22553610 | 2 |
| #22553593 | 2 |
| #22553510 | 2 |
| #22553439 | 2 |
| #22553413 | 2 |
| C4×#14523500 | 2 |
| #460×C131 | 2 |
| #3368 | 131 |