Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
310 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 35. #14581732 | Q8 | semidirect |
| 52. C2×C16×C83 | Q8 | semidirect |
| 54. #108×C83 | Q8 | semidirect |
| 133. C83 | #13460 | semidirect |
| 168. C2×C16 | Dic166 | semidirect |
| 173. #108 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917991 | 2 |
| #24909236 | 2 |
| C2×#19127523 | 2 |
| #24908254 | 2 |
| #24905577 | 2 |
| #24905548 | 2 |
| C83×#1383 | 2 |
| #13460 | 83 |