Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#16862246 | C2 | semidirect |
| 3. #22553225 | C2 | semidirect |
| 5. #22553178 | C2 | semidirect |
| 6. #22553169 | C2 | semidirect |
| 7. C4×C4⋊C4×C131 | C2 | semidirect |
| 28. C2×D524 | Q8 | semidirect |
| 90. C131 | #2563 | semidirect |
| 98. C4×C4⋊C4 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862246 | 2 |
| C2×C4×D524 | 2 |
| #22553225 | 2 |
| #22553214 | 2 |
| #22553178 | 2 |
| #22553169 | 2 |
| C4×C4⋊C4×C131 | 2 |
| #2563 | 131 |