Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
356 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 32. #14581732 | Q8 | semidirect |
| 46. M32×C83 | Q8 | semidirect |
| 48. #107×C83 | Q8 | semidirect |
| 127. C83 | #13457 | semidirect |
| 157. M32 | Dic166 | semidirect |
| 162. #107 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128098 | 2 |
| C2×#19127524 | 2 |
| C2×#19127523 | 2 |
| #24908212 | 2 |
| #24905568 | 2 |
| #24905544 | 2 |
| C83×#1386 | 2 |
| #13457 | 83 |