Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 41. #14581732 | Q8 | semidirect |
| 59. M32×C83 | Q8 | semidirect |
| 65. #106×C83 | Q8 | semidirect |
| 163. C83 | #13454 | semidirect |
| 202. M32 | Dic166 | semidirect |
| 218. #106 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917986 | 2 |
| #24909252 | 2 |
| #24909251 | 2 |
| #24908207 | 2 |
| #24905570 | 2 |
| #24905546 | 2 |
| C83×#1386 | 2 |
| #13454 | 83 |