Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22553276 | C2 | semidirect |
| 2. #22553175 | C2 | semidirect |
| 3. #22553046 | C2 | semidirect |
| 8. C22⋊(C131⋊C8) | C22 | semidirect |
| 10. C131⋊#95 | C22 | semidirect |
| 12. C22×D4×C131 | C4 | semidirect |
| 16. #121×C131 | C4 | semidirect |
| 18. C2×C4⋊C4×C131 | C4 | semidirect |
| 102. C131 | #1510 | semidirect |
| 109. C22×D4 | Dic131 | semidirect |
| 114. #121 | Dic131 | semidirect |
| 116. C2×C4⋊C4 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553276 | 2 |
| #22553175 | 2 |
| #22553046 | 2 |
| C2×#121×C131 | 2 |
| #1510 | 131 |