Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16862268 | C2 | semidirect |
| 2. #22553862 | C2 | semidirect |
| 3. #22553706 | C2 | semidirect |
| 4. #22553701 | C2 | semidirect |
| 5. C2×#97×C131 | C2 | semidirect |
| 32. C2×C8×C131 | D4 | semidirect |
| 63. C131 | #3150 | semidirect |
| 69. C2×#97 | D131 | semidirect |
| 94. C2×C8 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862268 | 2 |
| #22553862 | 2 |
| #22553706 | 2 |
| #22553701 | 2 |
| C2×#97×C131 | 2 |
| #3150 | 131 |