Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22553658 | C2 | semidirect |
| 2. #22553517 | C2 | semidirect |
| 3. D4×C131⋊C8 | C2 | semidirect |
| 4. #22553064 | C2 | semidirect |
| 5. #22553059 | C2 | semidirect |
| 6. #22553056 | C2 | semidirect |
| 84. C131 | #1681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553658 | 2 |
| #22553517 | 2 |
| D4×C131⋊C8 | 2 |
| #22553064 | 2 |
| #22553059 | 2 |
| #22553056 | 2 |
| #459×C131 | 2 |
| #1681 | 131 |