Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22554037 | C2 | semidirect |
| 4. #22553664 | C2 | semidirect |
| 5. #22553618 | C2 | semidirect |
| 7. #22553523 | C2 | semidirect |
| 8. #22553436 | C2 | semidirect |
| 9. #22553406 | C2 | semidirect |
| 115. C131 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554037 | 2 |
| #22554032 | 2 |
| #22553665 | 2 |
| #22553664 | 2 |
| #22553618 | 2 |
| #22553533 | 2 |
| #22553523 | 2 |
| #22553436 | 2 |
| #22553406 | 2 |
| C4×#14523501 | 2 |
| #474×C131 | 2 |
| #3364 | 131 |