Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
308 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 308 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 |
|---|---|---|
| 36. C2×C83⋊C16 | Q8 | semidirect |
| 52. C2×C16×C83 | Q8 | semidirect |
| 132. C83 | #13269 | semidirect |
| 170. C2×C16 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916403 | 2 |
| #24909228 | 2 |
| #24909067 | 2 |
| #24905550 | 2 |
| #24905548 | 2 |
| #24905543 | 2 |
| C83×#1375 | 2 |
| #13269 | 83 |