Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #22553717 | C2 | semidirect |
| 3. #22553593 | C2 | semidirect |
| 4. #22553517 | C2 | semidirect |
| 5. #22553057 | C2 | semidirect |
| 6. #22553041 | C2 | semidirect |
| 7. D4⋊C8×C131 | C2 | semidirect |
| 97. C131 | #1647 | semidirect |
| 105. D4⋊C8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553966 | 2 |
| #22553717 | 2 |
| #22553593 | 2 |
| #22553517 | 2 |
| #22553057 | 2 |
| #22553041 | 2 |
| D4⋊C8×C131 | 2 |
| #1647 | 131 |