Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #22553790 | C2 | semidirect |
| 4. #22553073 | C2 | semidirect |
| 5. C2×#101×C131 | C2 | semidirect |
| 8. #16862235 | C4 | semidirect |
| 79. C131 | #1888 | semidirect |
| 84. C2×#101 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862235 | 2 |
| #22553790 | 2 |
| #22553318 | 2 |
| #22553073 | 2 |
| C2×#101×C131 | 2 |
| #1888 | 131 |