Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #22553664 | C2 | semidirect |
| 3. #22553653 | C2 | semidirect |
| 4. #22553589 | C2 | semidirect |
| 5. #22553551 | C2 | semidirect |
| 6. #22553522 | C2 | semidirect |
| 7. #22553472 | C2 | semidirect |
| 8. C4×#14523500 | C2 | semidirect |
| 9. D4×C131⋊C8 | C2 | semidirect |
| 10. #22553306 | C2 | semidirect |
| 11. #556×C131 | C2 | semidirect |
| 125. C131 | #3302 | semidirect |
| 127. #556 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553967 | 2 |
| #22553664 | 2 |
| #22553653 | 2 |
| #22553589 | 2 |
| #22553551 | 2 |
| #22553522 | 2 |
| #22553472 | 2 |
| C4×#14523500 | 2 |
| D4×C131⋊C8 | 2 |
| #22553306 | 2 |
| #556×C131 | 2 |
| #3302 | 131 |