Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 91. Q8×C83 | Q32 | semidirect |
| 133. C83 | #12334 | semidirect |
| 221. Q8 | #14581738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920469 | 2 |
| #24909715 | 2 |
| #24909510 | 2 |
| #24905511 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| #24905426 | 2 |
| C83×#1670 | 2 |
| #12334 | 83 |