Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22553360 | C2 | semidirect |
| 2. #22553335 | C2 | semidirect |
| 5. #22553083 | C2 | semidirect |
| 6. #22553073 | C2 | semidirect |
| 15. #16862173 | C4 | semidirect |
| 16. #16862173 | C4 | semidirect |
| 97. C131 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553360 | 2 |
| #22553335 | 2 |
| #22553329 | 2 |
| C2×#16862173 | 2 |
| #22553083 | 2 |
| #22553073 | 2 |
| #568×C131 | 2 |
| #1861 | 131 |