Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 36. C2×C83⋊C16 | Q8 | semidirect |
| 38. #14581728 | Q8 | semidirect |
| 51. M32×C83 | Q8 | semidirect |
| 141. C83 | #13456 | semidirect |
| 172. M32 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918003 | 2 |
| C2×#19127528 | 2 |
| #24908246 | 2 |
| #24905572 | 2 |
| #24905558 | 2 |
| #24905553 | 2 |
| C83×#2159 | 2 |
| #13456 | 83 |