Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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×#16862234 | C2 | semidirect |
| 2. C2×#16862225 | C2 | semidirect |
| 4. #22553218 | C2 | semidirect |
| 5. #22553214 | C2 | semidirect |
| 6. #22553203 | C2 | semidirect |
| 7. #22553191 | C2 | semidirect |
| 8. #22553178 | C2 | semidirect |
| 9. C22×C42×C131 | C2 | semidirect |
| 63. C42×C131 | D4 | semidirect |
| 103. C22×C131 | #124 | semidirect |
| 128. C131 | #2850 | semidirect |
| 133. C22×C42 | D131 | semidirect |
| 192. C42 | C22⋊D131 | semidirect |
| 237. C22 | #16862234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862234 | 2 |
| C2×#16862225 | 2 |
| C2×#16862220 | 2 |
| #22553218 | 2 |
| #22553214 | 2 |
| #22553203 | 2 |
| #22553191 | 2 |
| #22553178 | 2 |
| C22×C42×C131 | 2 |
| #2850 | 131 |