Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14523503 | C2 | semidirect |
| 3. C2×C4×Dic262 | C2 | semidirect |
| 4. #22553531 | C2 | direct (N × H) |
| 5. C2×C4⋊(C131⋊C8) | C2 | semidirect |
| 6. C2×#16862170 | C2 | semidirect |
| 11. C2×#14523503 | C22 | semidirect |
| 17. C4×Dic262 | C22 | semidirect |
| 21. C4⋊(C131⋊C8) | C22 | semidirect |
| 22. #16862170 | C22 | semidirect |
| 111. C2×C131 | #464 | semidirect |
| 115. C131 | C2×#464 | semidirect |
| 227. C2 | #22553531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523503 | 2 |
| C22×#14523501 | 2 |
| C2×C4×Dic262 | 2 |
| #22553531 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C2×#16862170 | 2 |
| C2×#16862167 | 2 |
| C2×#124×C131 | 2 |
| C2×#464 | 131 |