Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22553077 | C2 | semidirect |
| 4. #22553076 | C2 | semidirect |
| 5. #341×C131 | C2 | semidirect |
| 69. C131 | #1738 | semidirect |
| 75. #341 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523496 | 2 |
| C2×M16×D131 | 2 |
| #22553077 | 2 |
| #22553076 | 2 |
| #341×C131 | 2 |
| #1738 | 131 |