Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862252 | C2 | semidirect |
| 2. #22553890 | C2 | semidirect |
| 3. #22553567 | C2 | semidirect |
| 4. #22553562 | C2 | semidirect |
| 5. #22553538 | C2 | semidirect |
| 6. C2×#16862178 | C2 | semidirect |
| 7. #22553313 | C2 | semidirect |
| 8. C2×#135×C131 | C2 | semidirect |
| 57. C2×C8×C131 | D4 | semidirect |
| 105. C131 | #3060 | semidirect |
| 107. C2×#135 | D131 | semidirect |
| 158. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862252 | 2 |
| #22553890 | 2 |
| #22553567 | 2 |
| #22553562 | 2 |
| #22553538 | 2 |
| C2×#16862178 | 2 |
| #22553313 | 2 |
| C2×#135×C131 | 2 |
| #3060 | 131 |