Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 34. #14581732 | Q8 | semidirect |
| 50. M32×C83 | Q8 | semidirect |
| 132. C83 | #13270 | semidirect |
| 166. M32 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916397 | 2 |
| #24909228 | 2 |
| #24909067 | 2 |
| #24905550 | 2 |
| #24905548 | 2 |
| #24905545 | 2 |
| C83×#1376 | 2 |
| #13270 | 83 |