Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 3. #22553139 | C2 | semidirect |
| 4. #22553117 | C2 | semidirect |
| 5. #22553115 | C2 | semidirect |
| 7. #367×C131 | C2 | semidirect |
| 66. C131 | #2235 | semidirect |
| 71. #367 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553554 | 2 |
| #107×D131 | 2 |
| #22553139 | 2 |
| #22553117 | 2 |
| #22553115 | 2 |
| (C2×D131)⋊C16 | 2 |
| #367×C131 | 2 |
| #2235 | 131 |