Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22553620 | C2 | semidirect |
| 4. #22553608 | C2 | semidirect |
| 5. #22553598 | C2 | semidirect |
| 37. C2×Dic262 | Q8 | semidirect |
| 106. C131 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553869 | 2 |
| C2×C4×Dic262 | 2 |
| #22553620 | 2 |
| #22553608 | 2 |
| #22553598 | 2 |
| #22553354 | 2 |
| #22553322 | 2 |
| #423×C131 | 2 |
| #3078 | 131 |