Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×C4×Dic262 | C2 | semidirect |
| 2. #22553645 | C2 | semidirect |
| 4. #22553616 | C2 | semidirect |
| 5. #22553531 | C2 | semidirect |
| 6. #22553467 | C2 | semidirect |
| 8. #22553417 | C2 | semidirect |
| 9. #22553412 | C2 | semidirect |
| 10. #22553369 | C2 | semidirect |
| 131. C131 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic262 | 2 |
| #22553645 | 2 |
| #22553628 | 2 |
| #22553616 | 2 |
| #22553531 | 2 |
| #22553467 | 2 |
| #22553450 | 2 |
| #22553417 | 2 |
| #22553412 | 2 |
| #22553369 | 2 |
| #529×C131 | 2 |
| #3117 | 131 |