Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16862276 | C2 | semidirect |
| 2. C2×#16862271 | C2 | semidirect |
| 3. C2×#16862234 | C2 | semidirect |
| 4. #22553704 | C2 | semidirect |
| 5. #22553699 | C2 | semidirect |
| 6. #22553694 | C2 | semidirect |
| 7. C4×#14523497 | C2 | semidirect |
| 8. #532×C131 | C2 | semidirect |
| 13. C2×#14523503 | C22 | semidirect |
| 14. C2×#14523501 | C22 | semidirect |
| 22. #16862157 | C22 | semidirect |
| 23. C4×C131⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C131 | C22 | semidirect |
| 26. #127×C131 | C22 | semidirect |
| 27. #124×C131 | C22 | semidirect |
| 43. #14523497 | D4 | semidirect |
| 106. C131 | #3153 | semidirect |
| 110. #532 | D131 | semidirect |
| 126. C4⋊Q8 | C2×D131 | semidirect |
| 127. #127 | C2×D131 | semidirect |
| 131. #124 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862276 | 2 |
| C2×#16862271 | 2 |
| C2×#16862234 | 2 |
| #22553704 | 2 |
| #22553699 | 2 |
| #22553694 | 2 |
| C4×#14523497 | 2 |
| #532×C131 | 2 |
| #3153 | 131 |