Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×Dic524 | C2 | semidirect |
| 3. C2×#16862246 | C2 | semidirect |
| 5. #22553706 | C2 | direct (N × H) |
| 6. C2×#97×C131 | C2 | semidirect |
| 11. C2×Dic524 | C22 | semidirect |
| 15. #16862246 | C22 | semidirect |
| 22. #97×C131 | C22 | semidirect |
| 78. C2×C131 | #497 | semidirect |
| 82. C131 | C2×#497 | semidirect |
| 89. C2×#97 | D131 | semidirect |
| 105. #97 | C2×D131 | semidirect |
| 162. C2 | #22553706 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic524 | 2 |
| C22×#14523502 | 2 |
| C2×#16862246 | 2 |
| C2×#16862234 | 2 |
| #22553706 | 2 |
| C2×#97×C131 | 2 |
| C2×#497 | 131 |