Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 656 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×#14523502 | C2 | semidirect |
| 2. C22×#14523501 | C2 | semidirect |
| 3. C22×#14523500 | C2 | semidirect |
| 4. C2×#16862244 | C2 | semidirect |
| 6. #22553683 | C2 | direct (N × H) |
| 7. C2×C8×Dic131 | C2 | semidirect |
| 8. C22×SD16×C131 | C2 | semidirect |
| 13. C2×#14523502 | C22 | semidirect |
| 15. C2×#14523501 | C22 | semidirect |
| 17. C2×#14523500 | C22 | semidirect |
| 20. #16862244 | C22 | semidirect |
| 25. C8×Dic131 | C22 | semidirect |
| 29. C2×SD16×C131 | C22 | semidirect |
| 47. C2×C131⋊C8 | D4 | semidirect |
| 64. C2×C8×C131 | D4 | semidirect |
| 78. C2×Dic131 | SD16 | semidirect |
| 80. C131⋊C8 | C2×D4 | semidirect |
| 97. C8×C131 | C2×D4 | semidirect |
| 112. Dic131 | C2×SD16 | semidirect |
| 114. C2×C131 | #492 | semidirect |
| 118. C131 | C2×#492 | semidirect |
| 123. C22×SD16 | D131 | semidirect |
| 140. C2×SD16 | C2×D131 | semidirect |
| 180. C2×C8 | C22⋊D131 | semidirect |
| 216. C8 | C2×C22⋊D131 | semidirect |
| 234. C2 | #22553683 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| C22×#14523501 | 2 |
| C22×#14523500 | 2 |
| C2×#16862244 | 2 |
| C2×#16862242 | 2 |
| #22553683 | 2 |
| C2×C8×Dic131 | 2 |
| C22×SD16×C131 | 2 |
| C2×#492 | 131 |