Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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×#14523497 | C2 | semidirect |
| 3. C2×#16862166 | C2 | semidirect |
| 4. #22553074 | C2 | semidirect |
| 5. #380×C131 | C2 | semidirect |
| 12. #16862220 | C4 | semidirect |
| 31. C2×C131⋊C8 | D4 | semidirect |
| 104. C131 | #1895 | semidirect |
| 109. #380 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523497 | 2 |
| C2×#16862220 | 2 |
| C2×#16862166 | 2 |
| #22553074 | 2 |
| #380×C131 | 2 |
| #1895 | 131 |