Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22554040 | C2 | semidirect |
| 4. #22553663 | C2 | semidirect |
| 5. #22553620 | C2 | semidirect |
| 8. #22553523 | C2 | semidirect |
| 9. C4×Dic524 | C2 | semidirect |
| 11. C8×Q8×C131 | C2 | semidirect |
| 115. C131 | #3364 | semidirect |
| 125. C8×Q8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554040 | 2 |
| #22554035 | 2 |
| #22553667 | 2 |
| #22553663 | 2 |
| #22553620 | 2 |
| #22553593 | 2 |
| #22553535 | 2 |
| #22553523 | 2 |
| C4×Dic524 | 2 |
| C4×#14523502 | 2 |
| C8×Q8×C131 | 2 |
| #3364 | 131 |