Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22553663 | C2 | semidirect |
| 4. #22553522 | C2 | semidirect |
| 5. #22553060 | C2 | semidirect |
| 7. Q8⋊C8×C131 | C2 | semidirect |
| 53. D524 | Q16 | semidirect |
| 88. C131 | #1644 | semidirect |
| 95. Q8⋊C8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554022 | 2 |
| #22553663 | 2 |
| #22553593 | 2 |
| #22553522 | 2 |
| #22553060 | 2 |
| #22553041 | 2 |
| Q8⋊C8×C131 | 2 |
| #1644 | 131 |