Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553656 | C2 | semidirect |
| 4. #22553655 | C2 | semidirect |
| 5. #22553649 | C2 | semidirect |
| 6. #22553644 | C2 | semidirect |
| 7. #22553355 | C2 | semidirect |
| 8. #22553320 | C2 | semidirect |
| 9. C2×#16862171 | C2 | semidirect |
| 11. #427×C131 | C2 | semidirect |
| 126. C131 | #3097 | semidirect |
| 135. #427 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553888 | 2 |
| #22553792 | 2 |
| #22553656 | 2 |
| #22553655 | 2 |
| #22553649 | 2 |
| #22553644 | 2 |
| #22553355 | 2 |
| #22553320 | 2 |
| C2×#16862171 | 2 |
| #22553278 | 2 |
| #427×C131 | 2 |
| #3097 | 131 |