Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
190 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22553034 | C2 | semidirect |
| 4. #22553034 | C2 | semidirect |
| 5. #22553033 | C2 | semidirect |
| 6. C8×C131⋊C8 | C2 | semidirect |
| 65. C131 | #1453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553365 | 2 |
| C4×#14523497 | 2 |
| #22553034 | 2 |
| #22553033 | 2 |
| C8×C131⋊C8 | 2 |
| #431×C131 | 2 |
| #1453 | 131 |