Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22554040 | C2 | semidirect |
| 3. #22553662 | C2 | semidirect |
| 4. #22553619 | C2 | semidirect |
| 7. #22553519 | C2 | semidirect |
| 8. Q8×C131⋊C8 | C2 | semidirect |
| 9. C4×#14523503 | C2 | semidirect |
| 115. C131 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554040 | 2 |
| #22553666 | 2 |
| #22553662 | 2 |
| #22553619 | 2 |
| #22553592 | 2 |
| #22553531 | 2 |
| #22553519 | 2 |
| Q8×C131⋊C8 | 2 |
| C4×#14523503 | 2 |
| C4×#14523501 | 2 |
| #556×C131 | 2 |
| #3364 | 131 |